Method and apparatus for estimating body shape

ABSTRACT

A system and method of estimating the body shape of an individual from input data such as images or range maps. The body may appear in one or more poses captured at different times and a consistent body shape is computed for all poses. The body may appear in minimal tight-fitting clothing or in normal clothing wherein the described method produces an estimate of the body shape under the clothing. Clothed or bare regions of the body are detected via image classification and the fitting method is adapted to treat each region differently. Body shapes are represented parametrically and are matched to other bodies based on shape similarity and other features. Standard measurements are extracted using parametric or non-parametric functions of body shape. The system components support many applications in body scanning, advertising, social networking, collaborative filtering and Internet clothing shopping.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims priority benefit of U.S. Provisional ApplicationNo. 61/189,118 filed Aug. 15, 2008 and titled Method and Apparatus forParametric Body Shape Recovery Using Images and Multi-Planar CastShadows, U.S. Provisional Application No. 61/107,119 filed Oct. 21, 2008and titled Method and Apparatus for Parametric Body Shape Recovery UsingImages and Multi-Planar Cast Shadows, and U.S. Provisional ApplicationNo. 61/189,070 filed Aug. 15, 2008 and titled Analysis of Images withShadows to Determine Human Pose and Body Shape.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with support from Grants NSF IIS-0812364 fromthe National Science Foundation, Grant NSF IIS-0535075 from the NationalScience Foundation, and Grant N00014-07-1-0803 from the Office of NavalResearch. The United States Government has certain rights in theinvention.

BACKGROUND OF THE INVENTION

The present invention relates to the estimation of human body shapeusing a low-dimensional 3D model using sensor data and other forms ofinput data that may be imprecise, ambiguous or partially obscured.

The citation of published references in this section is not an admissionthat the publications constitute prior art to the presently claimedsubject matter.

Body scanning technology has a long history and many potentialapplications ranging from health (fitness and weight loss), toentertainment (avatars and video games) and the garment industry (customclothing and virtual “try-on”). Current methods however are limited inthat they require complex, expensive or specialized equipment to capturethree-dimensional (3D) body measurements.

Most previous methods for “scanning” the body have focused on highlycontrolled environments and used lasers, millimeter waves, structuredlight or other active sensing methods to measure the depth of manypoints on the body with high precision. These many points are thencombined into a 3D body model or are used directly to estimateproperties of human shape. All these previous methods focus on makingthousands of measurements directly on the body surface and each of thesemust be very accurate. Consequently such systems are expensive toproduce.

Because these previous methods focus on acquiring surface measurements,they fail to accurately acquire body shape when a person is wearingclothing that obscures their underlying body shape. Most types ofsensors do not actually see the underlying body shape making the problemof estimating that shape under clothing challenging even whenhigh-accuracy range scanners are used. A key issue limiting theacceptance of body scanning technology in many applications has beenmodesty—most systems require the user to wear minimal or skin-tightclothing.

There are several methods for representing body shape with varyinglevels of specificity: 1) non-parametric models such as visual hulls(Starck and Hilton 2007, Boyer 2006), point clouds and voxelrepresentations (Cheung et al. 2003); 2) part-based models using genericshape primitives such as cylinders or cones (Deutscher and Reid 2005),superquadrics (Kakadiaris and Metaxas 1998; Sminchisescu and Telea 2002)or “metaballs” (Plankers and Fua 2003); 3) humanoid models controlled bya set of pre-specified parameters such as limb lengths that are used tovary shape (Grest et al. 2005; Hilton et al. 2000; Lee et al. 2000); 4)data driven models where human body shape variation is learned from atraining set of 3D body shapes (Anguelov et al. 2005; Balan et al.2007a; Seo et al. 2006; Sigal et al. 2007, 2008).

Machine vision algorithms for estimating body shape have typicallyrelied on structured light, photometric stereo, or multiple calibratedcamera views in carefully controlled settings where the use of lowspecificity models such as visual hulls is possible. As the imageevidence decreases, more human-specific models are needed to recovershape. In both previous scanning methods and machine vision algorithms,the sensor measurements are limited, ambiguous, noisy or do notcorrespond directly to the body surface. Several methods fit a humanoidmodel to multiple video frames, depth images or multiple snapshots froma single camera (Sminchisescu and Telea 2002, Grest et al. 2005, Lee etal. 2000). These methods estimate only limited aspects of body shapesuch as scaling parameters or joint locations in a pre-processing stepyet fail to capture the range of natural body shapes.

More realism is possible with data-driven methods that encode thestatistics of human body shape. Seo et al. (2006) use a learneddeformable body model for estimating body shape from one or more photosin a controlled environment with uniform background and with the subjectseen in a single predefined posture with minimal clothing. They requireat least two views (a front view and a side view) to obtain reasonableshape estimates. They choose viewing directions in which changes in poseare not noticeable and fit a single model of pose and shape to the frontand side views. They do not combine body shape information acrossvarying poses or deal with shape under clothing. The camera isstationary and calibrated in advance based on the camera height anddistance to the subject. They optimize an objective function thatcombines a silhouette overlap term with one that aligns manually markedfeature points on the model and in the image.

There are several related methods that use a 3D body model called SCAPE(Anguelov et al. 2005). While there are many 3D graphics models of thehuman body, SCAPE is low dimensional and it factors changes in shape dueto pose and identity. Anguelov et al. (2005) define the SCAPE model andshow how it can be used in several graphics applications. They dealtwith detailed laser scan data of naked bodies and did not fit the modelto image data of any kind.

In Balan et al. (2007a) the SCAPE model was fit to image data for thefirst time. They projected the 3D model into multiple calibrated imagesand compared the projected body silhouette with foreground regionsextracted using a known static background. An iterative importancesampling method was used to estimate the pose and shape that bestexplained the observed silhouettes. That method worked with as few as3-4 cameras if they were placed appropriately and calibrated accurately.The method did not deal with clothing, estimating shape across multipleposes, or un-calibrated imagery.

If more cameras are available, a visual hull or voxel representation canbe extracted from image silhouettes (Laurentini 1994) and the body modelcan be fit to this 3D representation. Mundermann et al. (2007) fit abody model to this visual hull data by first generating a large numberof example body shapes using SCAPE. They then searched this virtualdatabase of body shapes for the best example body that fit the visualhull data. This shape model was then kept fixed and segmented into rigidparts. The body was tracked using an Iterative Closest Point (ICP)method to register the partitioned model with the volumetric data. Themethod required 8 or more cameras to work accurately.

There exist a class of discriminative methods that attempt to establisha direct mapping between sensor features and 3D body shape and pose.Many methods exist that predict pose parameters, but only Sigal et al.(2007, 2008) predict shape parameters as well. Discriminative approachesdo not use an explicit model of the human body for fitting, but may usea humanoid model for generating training examples. Such approaches arecomputationally efficient but require a training database that spans allpossible poses, body shapes, and/or scene conditions (camera viewdirection, clothing, lighting, background, etc.) to be effective. Noneof these methods deal with clothing variations. Moreover the performancedegrades significantly when the image features are corrupted by noise orclutter. In such cases, a generative approach is more appropriate as itmodels the image formation process explicitly, where a discriminativeapproach is typically used for initializing a generative approach.

Grauman et al. (2003) used a 3D graphics model of the human body togenerate many training examples of synthetic people in different poses.The model was not learned from data of real people and lacked realism.Their approach projected each training body into one or more syntheticcamera views to generate a training set of 2D contours. Because thecamera views must be known during training, this implies that thelocations of the multiple cameras are roughly calibrated in advance (attraining time). They learned a statistical model of the multi-view 2Dcontour rather than the 3D body shape and then associated the differentcontour parameters with the structural information about the 3D bodythat generated them. Their estimation process involved matching 2Dcontours from the learned model to the image and then inferring therelated structural information (they recovered pose and did not show therecovery of body shape). Our approach of modeling shape in 3D is morepowerful because it allows the model to be learned independent of thenumber of cameras and camera location. Our 3D model can be projectedinto any view or any number of cameras and the shape of the 3D model canbe constrained during estimation to match known properties. Grauman etal. (2003) did not deal with estimating shape under clothing or thecombination of information about 3D body shape across multiplearticulated poses. Working with a 3D shape model that factors pose andshape allows us to recover a consistent 3D body shape from multipleimages where each image may contain a different pose.

None of the methods above are able to accurately estimate detailed bodyshape from un-calibrated perspective cameras, monocular images, orpeople wearing clothing.

Hasler et al. (2009c) are the first to fit a learned parametric bodymodel to 3D laser scans of dressed people. Their method uses a singlepose of the subject and requires the specification of sparse pointcorrespondences between feature locations on the body model and thelaser scan; a human operator provides these. They use a body model(Hasler et al. 2009b) similar to SCAPE in that it accounts forarticulated and non-rigid pose and identity deformations, but unlikeSCAPE, it does not factor pose and shape in a way that allows for thepose to be adjusted while the identity of body shape is kept constant.This is important since estimating shape under clothing is significantlyunder-constrained in a single pose case, combining information frommultiple articulated poses can constrain the solution. Their methodprovides no direct way to ensure that the estimated shape is consistentacross different poses. They require a full 360 degree laser scan and donot estimate shape from images or range sensing cameras.

BRIEF SUMMARY OF THE INVENTION

In accordance with the present invention, a system and method toestimate human body shape from sensor data where that data is imprecise,ambiguous or partially obscured is described. To make this possible, alow-dimensional 3D model of the human body is employed that accuratelycaptures details of the human form. The method fits the body model tosensor measurements and, because it is low-dimensional, many fewer andless accurate measurements are needed. It also enables the estimation ofbody shape under clothing using standard sensors such as digital camerasor inexpensive range sensors. Additionally the choice of parametricmodel enables a variety of new applications.

The present disclosure is directed to a system in which the sensor datais not rich and the environment is much less constrained that in priorsystems. These situations occur, for example, when standard digitalcamera images (e.g. cell phone cameras) are used as input and when onlyone, or a small number, of images of the person are available.Additionally these images may be acquired outside a controlledenvironment, making the camera calibration parameters (internalproperties and position and orientation in the world) unknown.

To recover body shape from standard sensors in less constrainedenvironments and under clothing, a parametric 3D model of the human bodyis employed. The term “body shape” means a pose independentrepresentation that characterizes the fixed skeletal structure (e.g.length of the bones) and the distribution of soft tissue (muscle andfat). The phrase “parametric model” refers any 3D body model where theshape and pose of the body are determined by a few parameters. Agraphics model is used that is represented as a triangulated mesh (othertypes of explicit meshes are possible such as quadrilateral meshes asare implicit surface models such as NURBS). A key property of anyparametric model is that it be low dimensional—that is, a wide range ofbody shapes and sizes can be expressed by a small number of parameters.A human body is complex and the number of vertices in a 3D mesh model ofthe body is often large. Laser range scans have 10's or 100's ofthousands of such vertices. The presently disclosed model captures thestatistical variability across a human population with a smaller numberof parameters (e.g. fewer than 100). To represent a wide variety ofhuman shapes with a low-dimensional model, statistical learning is usedto model the variability of body shape across a population (orsub-population).

With a low-dimensional model, only a few parameters need to be estimatedto represent body shape. This simplifies the estimation problem andmeans that accurate measurements can be obtained even with noisy,limited or ambiguous sensor measurements. Also, because a parametricmodel is being fitted, the model can cope with missing data. Whiletraditional scanners often produce 3D meshes with holes, the presentlydisclosed approach cannot generate models with holes and there is noneed to densely measure locations on the body to fit the 3D model. Onlya relatively small number of fairly weak measurements are needed to fitthe model and the recovered shape parameters explain any missing data.

Another property of the presently disclosed body model is that itfactors changes in body shape due to identity and changes due to pose.This means that changes in the articulated pose of the model do notsignificantly affect the intrinsic shape of the body. This factoringallows the combining of information about a person's body shape fromimages or sensor measurements of them in several articulated poses. Thisconcept is used to robustly estimate a consistent body shape from asmall number of images or under clothing.

In one embodiment, a method and system are described that enable therecovery of body shape even when a person is wearing clothing. Thisgreatly extends the useful applications of body shape recovery. Toestimate body shape under clothing, image classifiers are employed todetect regions corresponding to skin, hair or clothing. In skin regions,it is recognized that the actual body is being observed but in otherregions it is recognized that the body is obscured. In the obscuredregions, the fitting procedure is modified to take into account thatclothing or hair makes the body appear larger.

The presently disclosed method allows for fitting the body shape topartial depth information (e.g. from a time-of-flight sensor) that isrobust to clothing. Unlike a laser range scan, most range sensorsprovide information about depth on only one side of the object.Information can be gained about other views if the person moves andmultiple range images are captured. In this case one must deal withchanges in articulated pose between captures. The presently disclosedmethod estimates a single body model consistent with all views. Thedisclosed method further uses image intensity or color information tolocate putative clothed regions in the range scan and augments thematching function in these regions to be robust to clothing.

In many applications it is useful to employ just one or a small numberof images or other sensor measurements in estimating body shape.Furthermore with hand-held digital camera images, information about thecamera's location in the world is typically unknown (i.e. the camera isun-calibrated). In such situations, many body shapes may explain thesame data. To deal with this, a method is described for constrainedoptimization of body shape where the recovered model is constrained tohave certain known properties such as a specific height, weight, etc. Anew method is defined for directly estimating camera calibration alongwith body shape and pose parameters. When the environment can becontrolled however, other approaches to solving for camera calibrationare possible. Additionally, a method and apparatus are described thatuses “multi-chromatic keying” to enable both camera calibration andsegmentation of an object (person) from the background.

By construction, in the presently disclosed method every body modelrecovered from measurements is in full correspondence with every otherbody model. This means that a mesh vertex on the right shoulder in oneperson corresponds to the same vertex on another person's shoulder. Thisis unlike traditional laser or structured light scans where the meshtopology for every person is different. This formulation allows bodyshapes to be matched to each other to determine how similar they are;the method makes use of this in several ways. Additionally, it allowsseveral novel methods to extract standard tailoring measurements,clothing sizes, gender and other information from body scans. Unliketraditional methods for measuring body meshes, the presently disclosedmethods use a database of body shapes with known attributes (such asheight, waist size, preferred clothing sizes, etc) to learn a mappingfrom body shape to attributes. The presently disclosed method describesboth parametric and non-parametric methods for estimating attributesfrom body shape.

Finally, a means for body shape matching takes a body produced from somemeasurements (tailoring measures, images, range sensor data) and returnsone or more “scores” indicating how similar it is in shape to anotherbody or database of bodies. This matching means is used to rank bodyshape similarity to, for example, reorder a display of attributesassociated with a database of bodies. Such attributes might be items forsale, information about preferred clothing sizes, images, textualinformation or advertisements. The display of these attributes presentedto a user may be ordered so that the presented items are thosecorresponding to people with bodies most similar to theirs. The matchingand ranking means can be used to make selective recommendations based onsimilar body shapes. The attributes (e.g. clothing size preference) ofpeople with similar body shapes can be aggregated to recommendattributes to a user in a form of body-shape-sensitive collaborativefiltering.

Other features, aspects, applications and advantages of the presentlydisclosed system and method for estimating human body shape will beapparent to those of ordinary skill in the art from the DetailedDescription of the Invention that follows.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

The invention will be more fully understood by reference to the DetailedDescription of the Invention in conjunction with the accompanyingdrawings of which:

FIG. 1 is a block diagram depicting a data acquisition and fittingsub-system and a representation of a display and application subsystemshown in greater detail in FIG. 2 in accordance with the presentinvention;

FIG. 2 is a block diagram of a display and application sub-system and arepresentation of the acquisition and fitting subsystem of FIG. 1 inaccordance with the present invention;

FIG. 3 is a flow diagram illustrating a method for multi-chroma keycamera calibration and image segmentation;

FIG. 4 is a pictorial representation of a multi-chroma key environmentemploying two multi-colored grids;

FIG. 5 is a flow diagram illustrating a method for refining segmentationusing a projected 3D model and a tri-map of pixels;

FIG. 6 is a flow diagram depicting a method of performing discriminativebody shape and pose estimation;

FIG. 7 is a flow diagram depicting a method for initializing a bodyshape model from user-supplied measurements;

FIG. 8 depicts a clothed person in multiple poses;

FIG. 9 is a flow diagram depicting shape based collaborative filtering;

FIG. 10 depicts a flow diagram depicting method of obtaining a coarsesegmentation background and foreground images and utilizing the coarsesegmentation to obtain a course estimate of body shape and pose;

FIG. 11 depicts sample poses used for body shape estimation frommultiple images with changes in pose;

FIG. 12 depicts a flow diagram of a method for recovering a full bodymodel from several images, such as several snapshots obtained from ahandheld camera;

FIG. 13 is a flow diagram depicting a method of performing body shapematching of a potential buyer of goods to fit models that enables abody-shape sensitive display and ranking of products;

FIG. 14 is a block diagram depicting a system for determining theappropriate size for clothing displayed on a web page; and

FIG. 15 is a block diagram depicting a system for presenting informationto a user's web page based on matches between their body shape andconstraints specified by advertisers.

DETAILED DESCRIPTION OF THE INVENTION

The disclosures contained in following U.S. Provisional PatentApplications are hereby incorporated by reference:

a. U.S. Provisional Application No. 61/189,118 filed Aug. 15, 2008 andtitled Method and Apparatus for Parametric Body Shape Recovery UsingImages and Multi-Planar Cast Shadows.b. U.S. Provisional Application No. 61/107,119 filed Oct. 21, 2008 andtitled Method and Apparatus for Parametric Body Shape Recovery UsingImages and Multi-Planar Cast Shadows.c. U.S. Provisional Application No. 61/189,070 filed Aug. 15, 2008 andtitled Analysis of Images with Shadows to Determine Human Pose and BodyShape.

In the context of the present disclosure, the terms system, sub-system,component and/or process are used generally to refer to the functionsperformed and are not intended to imply any specific hierarchy withrespect to other referenced systems, sub-systems, components and/orprocesses discussed herein.

SECTION 1. SYSTEM OVERVIEW

FIGS. 1 and 2 provide an overview of the system. The two primarycomponents correspond to an acquisition and fitting sub-system (FIG. 1)and a display and application sub-system (FIG. 2). The major componentsare summarized here and then detailed descriptions appear in thesections that follow. Finally, the pieces of the system can be used asbuilding blocks to assemble several variants of the method describedhere. The system and methods are outlined using different numbers andtypes of sensors and then conclude with specific systems in severalfields.

The system 100 depicted in FIG. 1 may include one or more sensors suchas one or more digital cameras 101 a, time of flight sensors 101 b, IRsensors 101 c or any other suitable sensors 101 d. The system furtherincludes an environment instrumentation system 102, a data acquisitionsystem 103, a calibration and data pre-processing system 104, aninitialization system 105, a mechanism for providing user input 106, abody scan database 107, a statistical learning system 108, a parametricmodeling system 109, an optimization system 110. The system 100generates a fitted model 111 which may be displayed or provided to adisplay and application subsystem 112.

Sensors

Standard digital image sensors (e.g. CCD and CMOS) working in thevisible spectrum are typically employed although sensors working in thenon-visible spectrum may also be used. One or more measurements may betaken from one or more sensors and one or more instants in time. Thereis no requirement that all sensor measurements be taken at the same timeand, hence, the body pose may change between sensor acquisitions. Eachof these sensor acquisitions is referred to as a “frame” and it shouldbe understood that each frame could contain brightness measurements,depth measurements, surface normal measurements, etc. Multiple suchframes may be captured at a single time instant or multiple timeinstants and may come from a mixture of sensor types. The methodsdescribed here for combining information across pose, constraining bodyshape and fitting under clothing are applicable across many sensorsincluding laser scans, time-of-flight range images, infra red imagery,structured light scanners, visual hulls, etc. In all cases, the personcan be segmented from the background and the 3D model either fitdirectly to the observations (e.g. silhouettes or range data) orextracted features from the data.

Acquisition and Environmental Instrumentation

Data from the sensors is acquired and stored in memory in the dataacquisition system 103 where it is then processed by one or more CPUs.For calibration and segmentation described next, it is often useful topartially control the environment via environment instrumentation 102 tomake these processes easier. To that end we describe a newmulti-chromatic keying approach that combines the ideas of chroma-keyimage segmentation with camera calibration. The use of a specializedbackground pattern allows both processes to be performed simultaneously,obviating the need for a special calibration step. This is particularlyuseful in situations where the camera or the person is moving betweencaptured image frames or only a single image frame is captured.

Calibration and Data Pre-Processing System

In the calibration and data pre-processing system 104, images and othersensor data is typically segmented into foreground regions and, forestimating shape under clothing, regions corresponding to skin, clothingand hair are detected. Even with many range sensors, there is anassociated color image that can be used to detect skin or clothingregions. Previous methods for fitting body shape to images assumed thata static, known, background image is available to aid in segmentation ofthe foreground region. In general this is not possible with a smallnumber of camera views or a moving sensor. A method is disclosed hereinthat enables accurate segmentation.

The pre-processing may optionally detect regions of each frame thatcorrespond to skin, clothing or hair regions. A skin detection componentis used to identify skin regions where the body shape conforms to thesensor measurements. Skin detectors can be built from training datausing a simple non-parametric model of skin colors in hue and saturationspace. Standard image classification methods applied to visible imagedata though infra-red or other sensory input could be used to moreaccurately locate skin.

Additionally, fitting a 3D body to image measurements requires someknowledge of the camera calibration parameters. Since it is oftendesirable to deal with un-calibrated or minimally calibrated camerasseveral methods are described for dealing with this type of data. Insome situations, very little is known about the environment or cameraand, in these cases, more information is required about the subjectbeing scanned (e.g. their height). Such information may be provided viathe user data input system 106.

Initialization System

The estimation of body shape and pose is challenging and it helps tohave a good initial guess that is refined in the optimization process.Several methods are described herein. The simplest approach involvesrequiring the user to stand in a known canonical pose; for example, a“T” pose or a relaxed pose. An alternative method involves clicking on afew points in each image corresponding to the hands, feet, head, andmajor joints. From this, and information about body height (supplied viathe optional user input system 106), an estimation of an initial poseand shape is obtained. A fully automated method uses segmentedforeground regions to produce a pose and shape estimate by exploiting alearned mapping based on a mixture of linear regressors. This is anexample of a “discriminative” method that takes sensor features andrelates them directly to 3D body shape and pose. Such methods tend to beless accurate than the “generative” approach described next and henceare best for initialization. A method is also described for choosing anoptimal set of body measurements for estimating body shape from standardtailoring measurements or other body measurements.

Body Model

A database 107 of body scan information is obtained or generated. Onesuitable database of body scan information is known as the “CivilianAmerican and European Surface Anthropometry Resource” (CAESAR) and iscommercially available from SAE International, Warrendale, Pa. Given adatabase 107 of 3D laser ranges scans of human bodies, the bodies arealigned and then statistical learning methods are applied within thestatistical learning system 108 to learn a low-dimensional parametricbody model 109 that captures the variability in shape across people andposes. One embodiment employs the SCAPE representation for theparametric model taught by Anguelov et al. (2005).

Optimization

Given an optional initialization of shape and pose within theinitialization system 105, a fitting component provided in theoptimization subsystem 110 refines the body shape parameters to minimizean error function (i.e. cost function) defined by the distance betweenthe projected model and the identified features in the sensor data (e.g.silhouettes or range data). The fitting component includes a poseestimation component that updates the estimated pose of the body in eachframe. A single consistent body shape model is estimated from allmeasurements taken over multiple time instants or exposures (frames).The estimation (or fitting) can be achieved using a variety of methodsincluding stochastic optimization and gradient descent for example.These methods minimize an image error function (or equivalently maximizean image likelihood function) and may incorporate prior knowledge of thestatistics of human shapes and poses.

For image data, a standard image error function is implemented byprojecting the 3D body model onto the camera image plane. The error inthis prediction can be measured using a symmetric distance function thatcomputes the distance from projected regions to the observed imageregions and vice versa. For range data, a distance is defined in 3Dbetween the body model and each frame.

The above fitting can be performed with people wearing minimal clothing(e.g. underwear or tights) or wearing standard street clothing. Ineither case, multiple body poses may be combined to improve the shapeestimate. This exploits the fact that human body shape (e.g. limblengths, weight, etc.) is constant even though the pose of the body maychange. In the case of a clothed subject, we use a clothing-insensitive(that is, robust to the presence of clothing) cost function. Thiscaptures the fact that regions corresponding to the body in the frames(images or depth data) are generally larger for people in clothes andmakes the shape fitting sensitive to this fact. Combining measurementsfrom multiple poses is particularly useful for clothed people because,in each pose, the clothing fits the body differently, providingdifferent constraints on the underlying shape. Additionally, theoptional skin detection component within the calibration and datapre-processing system 104 is used to modify the cost function innon-skin regions. In these regions the body shape does not have to matchthe image measurements exactly.

The clothing-insensitive fitting method provides a way of inferring whatpeople look like under clothing. The method applies to standard cameraimages and/or range data. The advantage of this is that people need notremove all their clothes to obtain a reasonable body model. Of course,the removal of bulky outer garments such as sweaters will lead toincreased accuracy.

The output of this process is a fitted body model depicted at 111 thatis represented by a small number of shape and pose parameters. Thefitted model is provided as input to the display and applicationsub-system 112.

The display and application sub-system 112 of FIG. 1 is illustrated ingreater detail in FIG. 2. Referring to FIG. 2, the fitted model 111 maybe stored in a database 208 along with other user-supplied informationobtained via user input interface 106.

Display and Animation

The fitted model 111 is the output of the acquisition and fittingsub-system 100 depicted in FIG. 1. This model may be graphicallypresented on an output device (e.g. computer monitor, hand-held screen,television, etc.) in either static or animated form via a display andanimation subsystem 204. It may be optionally clothed with virtualgarments.

Attribute Extraction

In an attribute extraction subsystem 205, a variety of attributes suchas the gender, standard tailoring measurements and appropriate clothingsizes may be extracted from the fitted model. A gender identificationcomponent uses body shape to automatically estimate the gender of aperson based on their body scan. Two approaches for the estimation ofthe gender of a person are described. The first uses a gender-neutralmodel of body shape that includes men and women. Using a large databaseof body shapes, it has been determined that the shape coefficients formen and women, when embedded in a low dimensional gender-neutralsubspace, become separated in very distinctive clusters. This allows thetraining of simple gender classifiers and their use to predict genderfor newly scanned individuals based on shape parameters. A secondapproach fits two gender-specific models to the sensor measurements: onefor men and one for women. The model producing the lowest value of thecost function is selected as the most likely gender.

In one embodiment, the attribute extraction component 205 producesstandard biometric or tailoring measurements (e.g. inseam, waist size,etc.), pre-defined sizes (e.g. shirt size, dress size, etc.) or shapecategories (e.g. “athletic”, “pear shaped”, “sloped shoulders”, etc.).The estimation of these attributes exploits a database 208 that containsbody shapes and associated attributes and is performed using either aparametric or a non-parametric estimation technique.

Extracted attributes may be displayed or graphed using a display andanimation subsystem 204 or used as input to custom and retail clothingshopping applications as depicted by the shopping interface component206.

Matching

Given a fitted body model 111 and optional user input from the userinput interface 106, the model can be matched to a database 208 thatcontains stored 3D body models using a body shape matching component 207to produce a score for each model indicating how similar the fitted bodyis to each element (or a subset of elements) in the database. Thematching component 207 uses features of the body shape such as theparameters of the body shape model or shape descriptors derived from thevertices of the 3D body model. The match may also take into accountancillary attributes stored in the database 208 and provided by the uservia the user input interface 106 such as clothing and size preferences.

The match can be used to rank elements of a list using a score orranking component 209 for display by a display manager component 210.The list may contain associated bodies shapes and information such aspreferred clothing sizes, images, text, or advertising preferences. Thedisplay of the associated information may be aggregated from the bestmatches or may show a list of best matches with an optional match score.This enables a selective recommendation function where a person with onebody shape receives recommendations from a plurality of people withsimilar body shapes and attributes.

The database 208 of body shapes and attributes may include retailer oradvertiser specifications of body shapes and attributes along withassociated products or advertisements. The display manager 210 maypresent the products or advertisements to the user on any output device(e.g. graphical, auditory or tactile).

SECTION 2. CALIBRATION AND DATA PRE-PROCESSING

In the calibration and data pre-processing system 104 (FIG. 1) rawsensor data is transferred to memory where it is processed to extractinformation needed in later stages. Data processing includes the use oftechniques for segmenting a person from a background and for calibratingthe sensor(s).

2a. Foreground/Background Segmentation

A foreground segmentation component within the calibration and datapre-processing system 104 identifies the location of the person in aframe as distinct from the background. Standard techniques for imagedata use statistical measures of image difference between an image withand without a person present. For example, a standard method is to fit aGaussian distribution (or mixture of Gaussians) to the variation ofpixel values taken over several background images (Stauffer and Grimson1999). For a new image with the person present, a statistical test isperformed that evaluates how likely the pixel is to have come from thebackground model. Typically a probability threshold is set to classifythe pixel. After individual pixels have been classified as foreground orbackground, several image processing operations can be applied toimprove the segmentation, including dilation and erosion, medianfiltering, and removal of small disconnected components. More advancedmodels use Markov random fields to express prior assumptions on thespatial structure of the segmented foreground regions.

Alternatively, a statistical model of the background can be built as,for example, a color or texture histogram. A pixel can then beclassified by testing how likely it was to have come from the backgrounddistribution rather than a foreground distribution. (e.g. a uniformdistribution). This method differs from the one above in that thestatistical model is not built at the pixel level but rather describesthe image statistics of the background.

For range data, segmentation is often simpler. If a part of the body issufficiently far from the background, a simple threshold on depth can besufficient. More generally the person cannot be assumed to be distantfrom the background (e.g. the feet touch the floor). In these situationsa simple planar model of the background may be assumed and robustly fitto the sensor data. User input or a coarse segmentation can be used toremove much of the person. The remaining depth values are then fit bymultiple planes (e.g. for the ground and a wall). Standard robustmethods for fitting planes (e.g. RANSAC or M-estimation) can be used.Sensor noise can be modeled by fitting the deviations from the fittedplane(s); this can be done robustly by computing the median absolutedeviation (MAD). The foreground then can be identified based on itsdeviation from the fitted plane(s).

Information about segmentation from range and image values can becombined when spatially registered data is available.

2b. Camera Calibration Methods

Camera calibration defines the transformation from any 3D world pointX=[x, y, z]^(T) to a 2D image position U=[u, v]^(T) on an image sensor.Given the correct full calibration for a camera in its environment, theexact projection of any point in the world on the camera's sensor can bepredicted (with the caveat that some 3D points may not be in the frustumof the sensor). Practically, calibration encodes both extrinsicparameters (the position/rotation of the camera in the world coordinatesystem) and intrinsic parameters (field of view or focal length, lensdistortion characteristics, pixel skew, and other properties that do notdepend on camera position/orientation).

Assuming no lens distortion or that the images have been corrected forknown lens distortion, the relationship between X and U can be modeledwith the following homogeneous linear transformation

${{{\lbrack K\rbrack \begin{bmatrix}R & t\end{bmatrix}}\begin{bmatrix}x \\y \\z \\1\end{bmatrix}} = {{P\begin{bmatrix}x \\y \\z \\1\end{bmatrix}} = {\lambda \begin{bmatrix}u \\v \\1\end{bmatrix}}}},$

where K is the 3×3 intrinsic parameter matrix which is furtherparameterized in terms of focal length, principal point and skewcoefficient; R is the 3×3 rotation matrix of the camera; t is the 3×1vector denoting the position of the world origin in the coordinate frameof the camera; P is the 3×4 projection matrix; and λ is a homogeneousscale factor (Hartley and Zisserman 2000). Note that the extrinsicparameters of the camera consist of R and t. The full calibration iscomprised of the extrinsic and intrinsic parameters: ψ={R, t, K}.

One approach to calibration involves estimating some of the cameraparameters (extrinsic and/or intrinsic parameters) offline in a separatecalibration step using standard methods (Hartley and Zisserman 2000,Zhang 2000) that take controlled images of a known calibration object.This is appropriate for example when the camera is known to remainstationary or where its internal state is not changing during the livecapture session. Note however that setting up an initial calibrationstep is not always possible, as it is the case for calibratingtelevision images. In the case of a moving camera, the extrinsicparameters have to be estimated from the available imagery or ancillaryinformation such as inertial sensor data.

Calibration in a controlled environment involves detecting features inan image corresponding to a known (usually flat) 3D object in a scene.Given the 3D coordinates of the features in the object's coordinateframe, a homography H between the image plane and the plane of thecalibration object is computed (Zhang 2000). For a given set ofintrinsic parameters K (estimated online or offline), we use a standardmethod for upgrading the homography H to the extrinsic parameters R andt (Hartley and Zisserman 2000).

2c. Multi-Chroma Key Segmentation, Calibration, and Camera Tracking

Segmenting the image is easier when the environment can be controlled(or “instrumented”) such that foreground objects are easier to detect.The most historically popular approach to instrumented segmentation isthe Chroma Key method (otherwise known as “blue screening” or “greenscreening”), in which foreground items are photographed against abackground of known color (Smith and Blinn 1996; Vlahos 1978).

Similarly, calibration is easier when the environment is instrumented.For calibration, the most common method is to use images of a black andwhite checkerboard of known size whose corners in the image can easilybe extracted and used to compute the camera intrinsic and extrinsicparameters.

In the presently disclosed technique, these two procedures are combined.The idea is to calibrate the camera while the person is in the image andsegment the person from the background at the same time. One advantageof this approach is that no separate calibration step is needed.Additionally this allows the camera to move between each frame capture;that is, it allows the use of a hand-held camera. There are severaldifficulties with combining standard calibration methods with standardsegmentation methods. For accurate calibration the grid should occupy alarge part of the field of view. Similarly, for accurate body shapeestimation the person's body should occupy a large part of the field ofview. Consequently, capturing a person and a calibration object at thesame time means they are likely to overlap so that the person obscurespart of the calibration object. Another difficulty is that the personmust be segmented from the background and a standard black-whitecheckerboard is not ideal for this. Finally, the calibration grid mustbe properly identified even though it is partially obscured by theperson.

To address these problems a “Multi-Chroma Key” method is employed thatuses a known pattern with two or more colors (rather than the one colorused in Chroma Key). As with the standard Chroma Key method, thepresently disclosed method allows foreground/background segmentation.Additionally, the presently disclosed method also extends the standardChroma Key method to enable the recovery of camera calibrationinformation. Furthermore, the presently disclosed technique allowsreconstruction of a camera's 3D position and orientation with respect tothe physical scene as well as its intrinsic camera parameters such asfocal length, which allows important inference about ground planeposition and relative camera positioning between two adjacent shots orover an entire sequence. For example, tracking the 3D camera motionduring live action is important for later compositing withcomputer-generated imagery. The presently disclosed approach allows thestandard methods for Chroma Key segmentation to be combined with cameratracking.

First described is how the Multi-Chroma Key method can be used forcalibration given two background colors and occluding objects. Thetechnique is illustrated in FIG. 3. The segmentation of the person fromthe background is next described. The method has the following keycomponents: 1) identifying points on a multi-color grid; 2) fitting aplane to the grid and computing the extrinsic and intrinsic parameters;3) segmenting the background from the foreground. Many methods couldpotentially be used to implement these steps; we describe our preferredembodiment.

Environmental Instrumentation

Referring to FIGS. 3 and 4, surfaces are covered with a colored material(paint, fabric, board, etc.) that is static. These colored surfaces arereferred to as the environmental instrumentation 102. In one embodimenttwo large, flat surfaces are used, one behind the person as a backdrop401, and one on the floor 402, under the person's feet. A multi-tonepattern of precisely known size and shape is printed or painted on eachsurface. For best results, this pattern should avoid colors thatprecisely match those on the person in the foreground. In oneimplementation a checkerboard is used that alternates between blue andgreen, as shown in FIG. 4. The user 403 to be measured stands in frontof the instrumented background for capture. The size of the checkers canvary, as can as the number of rows and columns of the pattern, but bothshould be known to the system. The checkerboard can be embedded in alarger surface; the boundaries of said surface may be of solid color(e.g. blue or green).

Image Capture

Next, image capture 302 occurs with a digital camera 404, which may behand-held or moving and frames are stored to memory or to a disk. Theintrinsic parameters of the camera may be estimated in advance if it isknown they will not change. With known intrinsic parameters the image iscorrected for distortion (Hartley and Zisserman 2000).

Image Processing

Following image capture as depicted at block 302, image processing isperformed as illustrated at block 303. It is assumed that RGB (red,green, blue) input pixels {r_(i), g_(i), b_(i)}εI in the input image Iare constrained to the range [0,1] by the sensor. If this is not thecase (for example with 8-bit pixels) then the input pixel values arerescaled to the range [0,1].

Standard calibration methods assume a black and white checkerboardpattern. While this assumption can be relaxed, it is easy to convert themulti-chromatic grid into a black-white one for processing by standardmethods. To do so, the RGB pixel values are projected onto the line incolor space between the colors of the grid (i.e. the line between blueand green in RGB).

In the case of a blue-green grid, the color at each pixel in theoriginal image I is processed to generate a new gray-scale image Î.Pixels {ŝ_(i)}εÎ are computed from pixels {r_(i), g_(i), b_(i)}εI asfollows:

${\hat{s}}_{i} = {\frac{1}{2} + \frac{g_{i} - b_{i}}{2}}$

This results in a grayscale image which is brighter in areas that havemore green than blue, and darker in areas that have more blue thangreen. This allows the use of standard checkerboard detection algorithms(typically tuned for grayscale images) as described next.

Patch Detection

Following image processing as illustrated at block 303, grid patchdetection is performed as depicted at block 304 and described below.Pattern recognition is applied to this processed image Î in order todetect patches of the grid pattern. There are many methods that could beused to detect a grid in an image. Since the background may be partiallyoccluded by the user, it is important that the pattern recognitionmethod be robust to occlusion.

The OpenCV library (Bradski and Kaehler, 2008) may be employed for thecheckerboard detection function (“cvFindChessboardCorners”). Thisfunction returns an unordered set of grid points in image space wherethese points correspond to corners of adjacent quadrilaterals found inthe image. Because the person occludes the grid, it may be the case thatnot all visible points on the grid will be connected. Thus, only asubset of the grid points corresponding to a single connectedcheckerboard region is returned; this subset is called a “patch”. Wediscuss later on how to find the rest of the patches.

These image points on the patch must be put in correspondence withpositions on the checkerboard in order to find a useful homography.First, we identify four ordered points in the patch that form aquadrilateral; we follow the method described in Section II of (Rufli etal. 2008). Second, these points are placed in correspondence with thecorners of an arbitrary checkerboard square, from which a homography iscomputed (Zhang 2000). This homography still has a translation androtation ambiguity, although the projected grid lines still overlap. Weaccount for this ambiguity in the extrinsic computation stage 312.Third, to account for errors in corner detection, we refine thishomography via gradient descent to robustly minimize the distancesbetween all the homography-transformed grid points detected in the imageand their respective closest 3D points of an infinite grid.

Once the homography for a patch is found, the image area correspondingto the patch is “erased” so that it will no longer be considered:specifically the convex hull of the points in the image space iscomputed, and all pixels lying inside that space are set to 0.5 (gray).

The checkerboard detection process described above is then applied againfor the modified image to find the next patch of adjacent quadrilateralsand compute its homography. This is repeated until no additional cornersare found as depicted at block 305. This results in a collection ofpatches, each with an associated homography that is relative todifferent checkerboard squares.

Intrinsic Computation

The detected grid patches with associated homographies following patchdetection 304 can be used to estimate the intrinsic parameters of thecamera illustrated at block 316. This step is necessary only in the casewhen the intrinsic parameters have not already been estimated using anoffline calibration procedure. If at least two different views areavailable, the intrinsic parameters can be estimated (using the methodproposed by Zhang (2000)) from the set of all patch homographiesextracted in at least two different camera views. If only one view isavailable, intrinsic parameters may still be estimated from a set ofpatch homographies if common assumptions are made (zero skew anddistortion, principal point at the center of the image) (Zhang, 2000;Hartley and Zisserman, 2000). This estimation step is illustrated by box315.

Patch Consolidation

The total number of patches found in the patch detection step 304usually exceeds the number of planar textured surfaces in the scene. Inthe patch consolidation step 306, each patch is assigned to one of theplanar surfaces (the horizontal or vertical one). The homography foreach patch can be upgraded to full extrinsic parameters (see Section 2b)given intrinsic parameters.

Given the rotation of the camera with respect to this planar surface,every other patch is then classified as either “vertical” or“horizontal” with respect to the camera by examining the 3D normal ofthe patch in the coordinate system of the camera. Specifically, if thepatch normal is sufficiently close to being orthogonal with the camera'sup vector, then the patch is classified as “vertical”. This allows thegrouping of patches into two larger patches: a horizontal patch 307 anda vertical patch 308. This provides a large set of points classified as“vertical”, and a large set of points classified as “horizontal”, eachof which defines a large patch. A homography is computed for each of thelarge patches using the same method applied to the small patches duringthe patch detection step 304. This gives two homographies H_(v) andH_(h) 309.

Color Modeling

Given the image regions defined by the convex hull of each patch, amodel of the colors of the grids is computed 310 for image segmentation311. Note that if the grid colors are saturated, standard chroma-keymethods can be extended to deal with multiple colors and the followingstatistical modeling step can be omitted. In general lighting however,fitting the color distributions given the found patches is beneficial.

With patches on the grids located, two color distributions are modeled:one for the vertical patch, and one for the horizontal patch. Thesecorrespond to the collection of colors associated with the areas coveredby the smaller patches making up the larger ones. These smaller patchescan then be used to train color distributions: one two-componentGaussian mixture model (GMM) in hue-saturation-and-value (HSV) colorspace for the horizontal surface, and one two-component GMM for thevertical surface. Because the surfaces face in different directions withrespect to ambient lighting, they typically differ in the distributionof colors they generate.

Given these distributions, two probability images may be generated:T_(h) and T_(v). Note that T_(h) gives the probability of a pixel beinggenerated by the color distribution of the horizontal surface, andlikewise T_(v) represents the same properties for the vertical surface.By taking the per-pixel maximum T_(max) of the two probability imagesT_(h) and T_(v), we obtain an image that is used for the last steps ofthe process: obtaining extrinsic camera parameters, and obtainingsegmentation.

Segmentation

Segmentation is performed as depicted at block 311 to produce asegmented image 314 by thresholding T_(max). The threshold may beadjusted manually. This separates the image into a foreground region(below the threshold) and a background region (above the threshold).

Extrinsic Computation

This step is illustrated by box 312.

Single Frame Case:

In the case of single frame, where we are only interested in therelationship between the camera and the horizontal plane, it issufficient to upgrade H_(h) to {R_(h), t_(h)} via the method describedin Section 2b. This gives valid extrinsic parameters 313 relative to thehorizontal plane although the location and orientation of the boardinside the horizontal plane is ambiguous.

Multi-Frame Case (One Calibration Surface):

Shape estimation is better constrained from multiple camera views,however. Therefore, the case in which more than one frame is to becalibrated is now considered.

In this scenario, it is desirable to have a single world coordinateframe that relates all the camera views with consistent extrinsicparameters between views. Unlike the patch detection step 304, where thecorrespondence of a detected quadrilateral with the checkerboard wasestablished arbitrarily, here we need to search for the correctcorrespondence in each camera view. The following adjustment isperformed in order to compute the extrinsic parameters 313 with respectto a common coordinate system induced by the checkerboard. The keyconcept is to identify the entire board in the scene by matching it tothe found feature points.

Here we propose searching over all possible ways an image quadrilateraldetected in 304 can be matched with a checkerboard square. Given apattern of M×N squares, where M and N are assumed known, there are atotal of 4MN possible pairings: there are MN squares and four possibledirections the quadrilateral may be “facing”. To resolve ambiguities inthe cardinal direction of the grid pattern, we recommend usingrectangular grid patterns with even, but different, number of rows andcolumns, although symmetric patterns can also be handled in cases wherecamera motion between frames is relatively small. For each possiblequadrilateral correspondence, we obtain a different homography H_(h)using the method detailed in the patch detection step 304, which is thenupgraded to the extrinsic parameters {R_(h), t_(h)} via the methoddescribed in Section 2b. Using the colors of the surface (as discoveredvia GMM in the color modeling step) and the extrinsic parameters, thecalibration surface is rendered in each fully viewable candidateconfiguration (we assume the surface is completely within the camerafrustum). Each rendered calibration surface is then compared with theobserved image in the region of the rendered surface by finding theaverage absolute difference between the rendered pixels and the observedimage pixels. The hypothesized camera configuration with the lowest suchdifference is selected. Other methods for robustly finding the grids inthe image may be used and can be easily extended to detect grids whenonly part of the grid is visible in the image.

It should be noted that each such candidate configuration simply amountsto different horizontal translations and vertical orientations of theoriginal camera (specified by {R_(h),t_(h)}), each transformation beingaxis-aligned to the world coordinate system, and each translation beingan integer multiple of the real-world width of the squares.

In the case of a video sequence of images, it is possible to takeadvantage of the small variations in camera extrinsic parameters betweenconsecutive views and effectively perform grid tracking. Having locatedthe grid in one frame, it is robustly tracked over subsequent frames andthis gives corresponding corner locations. This eliminates the need forthe exhaustive search described above.

Multi-Frame Case (Multiple Calibration Surfaces):

Although the multi-frame process results in consistent extrinsicparameters for each view, better results can be obtained byincorporating a second, non-coplanar, calibration surface (e.g. thevertical calibration surface). The steps for incorporating theadditional surface are as follows.

First, for each frame, an estimate of the extrinsic parameters for theadditional surface is obtained in the same manner as for the firstsurface. This gives {R_(v), t_(v)} in addition to the already computed{R_(h), t_(h)} for each view. This is over-parameterized, as the spatialrelationship between the two surfaces is assumed constant (but unknown)between the frames. Therefore, the minimal set of extrinsic parametersincludes {R_(h), t_(h)} for each view, and one instance of {R_(L),t_(L)}, which specifies the extrinsic parameters of the additionalsurface with respect to the first surface. Because extrinsic parameterscan be specified with six degrees of freedom, this makes the totalnumber of parameters to estimate (6w+6), where w is the number offrames. These parameters can be optimized with gradient descent tominimize re-projection error of the image-space points found duringpatch detection 304.

This two-surface method can be extended to find a plurality of surfaces.

More General Formulations

The apparatus need not use a checkerboard or other symmetric pattern.Any known pattern will suffice and, in fact, introducing non-symmetricpatterns removes ambiguities in the detection and fitting of thepatterns. As an example, a non-symmetric pattern can be created bytaking random pairs of grid locations and making them the same color;the result is a pattern with non-square elements.

Also the surfaces need not be planar, though planar surfaces make thecomputation of camera parameters from a single frame easier. In the caseof non-planar surfaces an irregular pattern is preferred so thatcorrespondence of feature points between frames may be unambiguouslyestablished. This allows the tracking of many feature points over timeand the use of standard structure from motion algorithms to compute thecamera parameters essentially the multi-chroma surface provides a dense“texture” that is visible for the purpose of camera motion trackingwhile being “invisible” for the purpose of foreground segmentation. Thisgeneral formulation is particularly appropriate for standard filmapplications on a large set where camera motion must be tracked for thelater insertion of graphics characters with live footage.

It should be recognized that the presently disclosed technique forperforming calibration and segmentation may be applied to objectsgenerally, such as human bodies, animals, inanimate objects or otherbackground occluding objects.

Section 2d. Tri-Map Segmentation

In many cases it is not always possible or feasible to fullyinstrumented environment to make segmentation simple. For example ascanner in a changing room can be constructed such that the walls arepainted or wallpapered with a blue and green pattern. Even so, a simplebackground cannot be guaranteed since the user might hang clothes on thewall or place them on the floor. In this case a tri-map basedsegmentation method is described to obtain the foreground region.

Given the initial shape and pose (either from fitting the body modelcoarsely, with only the first few shape coefficients and an approximate3D pose of the body or from an initial low accuracy segmentation or bymanual initialization) 501, we find an initial set of pixels that arelikely to be inside the body that are then refined. One method projectsthe model into the image to create a 2D silhouette. This silhouette isthen dilated and eroded by several pixels (the number may be a functionof the image size) 502. This creates a “tri-map” of pixels 503 that arevery certain to be inside and outside the body as well as pixels thatare uncertain. Given such a tri-map 503, we use a standard segmentationmethod 504 such as GrabCut (Rother et al. 2004) to segment each inputimage into a refined foreground/background segmentation 505.

Section 2e. Image Skin Detection and Segmentation

There are many algorithms in the literature that perform skin detection(e.g. Jones and Rehg 2002). Many of these deal with variations inlighting and skin tone across different people and can be quiteaccurate. Clothing detection is a harder problem due to the widevariability of materials, colors, and patterns used to make clothing.Hair detection has also received some attention. In our case, skin andhair detection is sufficient to constrain the remainder of theforeground region to be classified as “clothing”. Skin and clothingregions will be treated differently in the fitting process.

A method is described for segmenting an image into skin and non-skinregions, although the precise formulation is not critical. In order todetect skin colored regions in an image, a skin detector can be builtfrom training data using a simple non-parametric model of skin pixels inhue and saturation space. By switching from the RGB to the HSV colorspace, the Value channel can be ignored, which captures mostly lightingintensity information. Using a large dataset of images that have beensegmented into skin or non-skin, a normalized joint histogram (H,S|skin)of Hue and Saturation values is built for the skin pixels. A thresholdon the histogram is used to obtain a binary skin classifier for (Hue,Saturation) pairs: P(H, S|skin)≧threshold .

After individual pixels have been classified as being skin or not skin,several standard image filters are applied to improve the segmentation,including dilation, median filtering, and removal of small disconnectedcomponents.

SECTION 3. BODY MODEL

In one embodiment, a parametric 3D body model called SCAPE (Anguelov etal., 2005) is employed. SCAPE is a deformable, triangulated mesh modelof the human body that accounts for different body shapes, differentposes, and non-rigid deformations due to articulation. For visionapplications, it offers realism while remaining relatively lowdimensional. It also factors changes in body shape due to identity andchanges due to pose.

It has been observed that SCAPE has many desirable properties but otherdeformable graphics models exist in the literature. Synthetic bodymodels can be generated using specialized commercial software tools(e.g. 3D Studio Max, BodyBuilder, Maya, Poser). The shape is controlledthough a number of parameters while pose is varied by associating thesurface mesh with a kinematic skeleton. While such models are easy toanimate, and allow for pose and shape to be altered independently, theresulting shapes often lack realism.

Most realistic models learn either the deformations due to pose or dueto identity changes from example 3D body scans, but not both. They useincompatible representations that make merging the two deformationmodels difficult. For example, Allen et al. (2002) learn a model of posedeformations using point displacements from an underlying articulatedmodel and focus on a single subject, while Allen et al. (2003) and Seoet al. (2003) model identity changes as point displacements from anaverage shape, embedded in a linear subspace. The latter however can beanimated using procedural skinning techniques but cannot capture musclebulging and creates twisting artifacts at the joints.

In addition to SCAPE, two other models are known that are able tocombine learned pose and learned identity shape changes. Allen et al.(2006) learn a complex system that combines corrective skinning learnedfrom examples with a latent model of identity variation. Unfortunatelythe complexity of the proposed training phase limits the amount oftraining data that can be used, which consequently impairs the model'srealism.

Hasler et al. (2009a) proposed a representation that couples pose andidentity shape deformations into a single linear subspace, where thedeformations are based on an encoding that is locally invariant totranslation and rotation. However, their model lacks the property ofbeing able to factor changes due to pose from changes due to identity,which is necessary for estimating a consistent shape across differentposes.

While not as realistic as SCAPE, any of these parametric models or othersuitable parametric models that factor pose and shape can be usedinstead. In particular, the simpler body model can be used to obtain aninitial estimate of the pose and shape which optionally can be refinedusing a more realistic model such as SCAPE.

SCAPE Model

The SCAPE model is derived from a large training set of human laserscans, which have been brought in full correspondence with respect to areference mesh, and implicitly with each other (Allen et al. 2003,Anguelov et al. 2005, Seo et al. 2003, Hasler et al. 2009b). By this,what is meant, for example, is that a mesh vertex on the right shoulderin one person corresponds to the same vertex on another person'sshoulder. It also means that all aligned meshes have the same number ofvertices and triangles. We use a reference mesh with V=12,500 verticesand T=25,000 triangles (Balan et al., 2007a) though both finer andcoarser meshes may be used. The strength of SCAPE comes from the way itrepresents deformations, using shape deformation gradients between areference mesh and other instance meshes. Shape deformation gradientsare 3×3 linear transformations specific to each triangle that can becombined in a multiplicative way. This gives SCAPE the ability to modelpose and body shape deformations separately and then combine the twodifferent deformation models in a natural way.

New body shapes and poses can be created by taking a reference 3D bodytemplate mesh X and applying a series of transformations to its edges toderive a new body mesh Y with a new shape and pose. Let (x_(t,1),x_(t,2), x_(t,3)) be the vertices of a triangle belonging to thetemplate mesh X and (y_(t,1), y_(t,2), y_(t,3)) be the correspondingtriangle from a new body mesh Y. Following Anguelov et al. (2005), twoedges of a triangle starting at x_(t,1) as Δx_(t,e)=x_(t,e)−x_(t,1),e=2,3 are defined. The deformation of one mesh to another is modeled asa sequence of linear transformations or deformations (described below)applied to the triangle edges of the template mesh:

Δy _(t,e) =R _(p[t])(θ)D _(t) ^(U,μ)(β)Q _(t) ^(α)(θ)Δx _(t,e).

A new mesh Y is created from the transformed triangles of X by solving aleast squares optimization problem

${Y\left( {\beta,\theta} \right)} = {\underset{\{{y_{1},\; \ldots \mspace{11mu},y_{V}}\}}{argmin}{\sum\limits_{t = 1}^{T}\; {\sum\limits_{{e = 2},3}\; {{{{{R^{p{\lbrack t\rbrack}}(\theta)}{D_{t}^{U,\mu}(\beta)}{Q_{t}^{\alpha}(\theta)}\Delta \; x_{t,e}} - {\Delta y}_{t,e}}}^{2}.}}}}$

Articulated deformations. Assuming that the mesh triangles are assignedto P individual body parts, we rotate the parts to produce the desiredjoint angle configuration defined by θ. R_(p[t])(θ) is a rigid 3×3rotation applied to each triangle t corresponding to a particular bodypart p. We take P=15 corresponding to the head, torso, pelvis, upper andlower arms and legs, hands and feet. Additional parts can be defined;for example the torso can be divided into several parts (Anguelov et al.2005).Non-rigid pose-induced deformations. Transforming a mesh according tothe articulated rigid transformation above results in a new mesh thatdoes not capture the non-rigid deformations associated with complexjoints such as the shoulder, muscle budging, and deformation of softtissue. The approach taken by Anguelov et al. (2005) was to learn alinear predictor of pose-dependent deformations used to correct the bodyshape for any non-rigid pose-dependent shape change. Q_(t) ^(α)(θ) is alearned 3×3 linear transformation matrix specific for a given triangle tcorresponding to non-rigid pose-induced deformations such as musclebulging; this is implemented as a linear function with linearcoefficients α of the rigid rotations of the two neighboring body parts.The linear coefficients α are learned from training scan data of asingle subject scanned in 70 different poses with known partorientations. The learned deformations predict the deviations from thearticulated rigid transformation to the observed laser scan.Body shape deformations. Finally, the shape of the person is changed byapplying a linear 3×3 shape deformation D_(t) ^(U,μ)(β) to each trianglein the mesh. Given a template mesh aligned with example bodies, thedeformation for each triangle in the template is computed to thecorresponding triangle in each example mesh. A low-dimensional,parametric, model is sought that characterizes these variations within apopulation of people.

A training set is constructed of body shape deformations between thetemplate mesh and over 2000 body scans of North American adults withroughly equal gender representation (Civilian American and EuropeanSurface Anthropometry Resource (CAESAR), SAE International. For a givenmesh, the body shape deformations for all triangles are concatenatedinto a single column vector and every example body becomes a column in amatrix of deformations. Incremental principal component analysis (PCA)(Brand, 2002) is used to find a reduced-dimension subspace that capturesthe variance in how body shapes deform. The first n principal componentsare used to approximate the vector of deformations as D^(U,μ)(β)=Uβ+μwhere μ is the mean body shape, U are the first n eigenvectors given byPCA and β is a vector of linear coefficients that characterizes a givenshape; in one embodiment n=20 though more bases can be used to increaseshape accuracy. The variance of each shape coefficient β_(j) is given bythe eigen-values σ_(β,j) ² obtained by PCA.

In contrast to the original SCAPE formulation, separate eigen-models arelearned for over 1,000 male and 1,000 female subjects respectively(Allen et al. 2003), as well as a gender-neutral model with all thesubjects combined:

D(χ,β^(χ))=U ^(χ)β^(χ)+μ^(χ), where χε{male,female,neutral}.

The variable χ denotes the gender model used. For the CAESAR dataset,the first n=20 principal components account for roughly 70% of the bodydeformation variance in the gender-neutral case and 65% of the variancein the gender specific cases.

For the remainder of the document, whenever the choice of gender modelcan either be inferred from the context or is not critical to thediscussion, the χ gender superscript χ is omitted.

Mesh transformation. A new mesh Y, not present in the training set, iscomputed from the desired joint angles θ, shape coefficients β andgender χ by solving

${Y\left( {\chi,\beta^{~\chi},\theta} \right)} = {\underset{\{{y_{1},\ldots \mspace{14mu},y_{v}}\}}{\arg \; \min}{\sum\limits_{t = 1}^{T}\; {\sum\limits_{{e = 2},3}\; {{{{{R^{p{\lbrack t\rbrack}}(\theta)}{D_{t}^{U^{\chi},\mu^{\chi}}\left( \beta^{\chi} \right)}{Q_{t}^{\alpha}(\theta)}\Delta \; x_{t,e}} - {\Delta \; y_{t,e}}}}^{2}.}}}}$

This optimization problem can be expressed as a linear system that canbe solved efficiently using linear least-square regression techniques.It is noted that this formulation leaves unconstrained threetranslational degrees of freedom. Therefore the global position of themesh also needs to be specified and, for notational convenience, theseparameters are included in the parameter vector θ.

SECTION 4. INITIALIZATION OF BODY POSE AND SHAPE

Estimating body shape and pose is challenging in part due to the highdimensional nature of the problem. Body pose may be described byapproximately 40 parameters while shape may be described by 20-100 ormore. Searching such a space is computationally challenging and is mademore difficult when the sensor input is noisy (e.g. time of flight depthdata) or ambiguous (e.g. monocular image silhouettes).

One way to make the optimization of body shape and pose practical is toinitialize the search near the true solution. This initializationcomponent can take several forms depending on the application domain. Ifthe initialization step is sufficiently accurate, it may not benecessary to perform an additional optimization step.

The initialization of body pose can be accomplished in a number of ways.Four cases are described. A simple case is described where the subjectis directed to stand in a particular pose and so the articulated poseinitialization is known a priori, leaving only the global pose to berecovered (Section 4a). A method is described for obtaining both theglobal and articulated pose from user input (Section 4b). Adiscriminative method is described for finding the 3D pose directly from2D image evidence (Section 4c). Other initialization methods could beemployed, such as using coarser body models which allow for anefficient, albeit less accurate, search over a larger space of poses, asdescribed in (Balan et al. 2007a), and then initializing the presentmodel from the coarser method's result. Finally, a method is alsodescribed herein for initialization of body shape based on measurements(Section 4d).

4a. Constraining the Set of Body Poses

In many applications it is possible to have people stand in one or more,fixed, known poses. This simplifies the initialization significantly. Ifthe pose parameters are assumed known, then one can solve for the rigid3D transformation that aligns the body with the image evidence. Thismethod has the following steps:

1. Choose an initial body shape. This can be the overall mean shape orthe mean shape for a particular sub-population, if this is known (e.g.women or men). A more detailed shape initialization method is definedbelow (Section 4d).2. Pose the 3D body model with this initial shape in the known pose.3. Solve for the 3D position and orientation of the body in thereference coordinate system using any of the standard optimizationmethods, but keeping articulated pose and shape parameters fixed. Tosolve for 3D position, the optimization method discussed in Section 6that follows can be used by simply keeping the pose and shape parametersfixed. If the environment is constrained, the 3D position andorientation may be approximately known, in which case this step isskipped.

Given this starting point, the body shape and pose is refined (Section6).

4b. Initialization of Body Pose from Clicked Points

It is possible to obtain an initial 3D body pose from user input. A usercould specify the initial pose directly, for example using a 3D modelinginterface, but it is desirable to provide an interface such that anon-expert user can specify the initial pose with a minimum of effort.Taylor (2000) described a method for such an method from a single image,where the user clicks on major joints in the image and providesinformation about whether each limb is extending out from the imageplane or receding into it; given known limb lengths, he reconstructs aplausible 3D pose, under the assumption that the camera is orthographic.Lee and Chen (1985) described a similar method under the assumption of aperspective camera, which they demonstrated only on noiseless, syntheticdata, allowing them to obtain necessary information about theperspective camera calibration in a manner that is infeasible for realimagery. Presently disclosed is an implementation that works on a widevariety of real images that also initializes body shape.

In accordance with the present teachings, a skeleton is defined that iscomposed of major joints that the user should be able to readilyidentify in the image, and the line segments connecting them which arereferred to as limbs. If the 3D position of the joint at one end of thelimb and the length of the limb are known, then the position of theother end of the limb must lie on a sphere, centered on the known jointwith a radius equal to the limb length. Given a clicked point in theimage plane and a method for projecting a camera ray corresponding tothat clicked point into 3-space (Hartley and Zisserman 2000), the end ofthe limb is located using ray-sphere intersection. There are, of course,three possibilities: the ray can intersect the sphere at zero, one, ortwo points. If there are two intersections, they correspond to the limbextending out from the image plane or receding into it; the user caneasily disambiguate these two cases and indicate which case is presentusing a graphical interface (GUI). If there is a single point ofintersection, then the limb lies exactly in the image plane and thelocation of the end point is not ambiguous, but due to numericalprecision, this is unlikely in practice. Finally, if there are nointersections, then the clicked point, the limb length, and the knownjoint position are inconsistent; an error is presented to the user andthe user is allowed to readjust the point.

Taylor (2000) assumes that the camera is orthographic, which providesseveral advantages: finding the ray for a given clicked point is trivialand depth becomes relative, so he can simply fix one joint to a depth of0. From this first, or root joint, he traverses the body skeleton,taking all limbs associated with the root joint and locating theirendpoints; he then takes each of those newly located endpoints andfollows the remaining limbs from them to locate their other ends, and soon until he has located all joints. Unfortunately, plausible results areonly achieved where the orthographic assumption is close to valid, forexample in photos taken with a telephoto lens.

Extending this to the case of a perspective camera allows plausible 3Dposes to be found from a wide variety of images, but requires twoadditional items. In order to model the perspective camera, its focallength needs to be known and a way to locate the depth of one of thejoints from which to traverse the skeleton and recover the pose isneeded. The focal length is often encoded in the image EXIF metadata andcan be easily extracted. When it is not, allowing the user to select areasonable focal length, for example with a graphical interface, oftenleads to more accurate pose estimates than simply making theorthographic assumption. The average focal length over a set of exampleimages can also be used and is often sufficient for initialization.

Locating the first (root) joint in 3D is a more difficult problem andhas not been previously addressed. Some assumptions need to be made inorder for the problem to be well defined. One tractable assumption isthat one limb lies in the image plane; a relaxed version of thisassumption can be used where the user varies the protrusion of this limbinteractively, for example using a graphical interface (e.g. a sliderthat controls a graphics simulation illustrating said protrusion). Thelimb that is the closest to lying in the image plane is detected byexamining the ratio of the 2D distance, d, between clicked points andthe 3D limb lengths, l. The limb whose ratio d/l is the largest is theclosest to lying in the image plane. The depth is then found using aratio of similar triangles.

One limitation of the methods of both Taylor (2000) and Lee and Chen(1985) is the assumption that limb lengths are known a priori. Thisassumption is relaxed in the present invention by employing astatistical model of human shape built from a database of scans of realhumans. For a given pose, limb lengths are defined as a linear functionof the vertices of a mesh transformed into that pose. Anthropometricdata such as height and weight specified by the user are obtained tofind an estimated body shape (Section 4d, below) and thus approximatelimb lengths specific to the person.

If range data is available with known spatial relationship to thevisible image data, the clicked points in the visible image can bedirectly mapped to the 3D range data. This greatly simplifies theinitialization because the ambiguities about the depth of the points areremoved. The pose of the body skeleton can be optimized so that the 3Dlocation of the joints directly fit the 3D measurements. Alternatively,the user can specify (click) the points directly on a visualpresentation of the range data.

4c. Learned Mapping from Features to Shape and Pose

Automatic initialization of the body shape and pose can be obtained bydirectly fitting a mathematical model relating image measurements tobody shapes and poses. This is an example of a discriminative method.Such methods have been used for estimating body pose (Agarwal and Triggs2005, 2006; Kanaujia et al. 2007; Poppe and Poel 2006; Sminchisescu etal. 1999, 2006) but not body shape; in fact, they are specificallydesigned to be invariant to body shape variations. The first knowndescription of a discriminative method for body shape estimation isdiscussed in Sigal et al. (2007, 2008).

Discriminative approaches to pose estimation attempt to learn a directmapping from image features to 3D pose from either a single image(Agarwal and Triggs 2006; Rosales and Sclaroff 2002; Sminchisescu et al.2005) or multiple approximately calibrated views. These approaches tendto use silhouettes (Agarwal and Triggs 2006; Rosales and Sclaroff 2002)and sometimes edges (Sminchisescu et al. 1999, 2006) as image featuresand learn a probabilistic mapping in the form of Nearest Neighbor (NN)search, regression (Agarwal and Triggs 2006), mixture of regressors(Agarwal and Triggs 2005), mixture of Bayesian experts (Sminchisescu etal. 2005), or specialized mappings (Rosales and Sclaroff 2002). Whileeffective and fast, they are inherently limited by the amount and thequality of the training data. More importantly they currently do notaddress estimation of the 3D body shape itself. The deficiencies of thecurrent models for discriminative pose estimation are addressed by thepresent invention to deal with the estimation of 3D body shape. Aprobabilistic model is introduced from which samples are drawn, andthese samples can be used as initial estimates for a generative bodyshape optimization method (Section 6).

Grauman et al. (2003) use a combination of generative and discriminativemethods. For a multi-view set of 2D image contours they use a generativeapproach to match a learned multi-view-contour model to the image data(i.e. they solve for the parameters of the low-dimensional contourmodel). Given the training data associating 2D contours with 3D models,they use the parameters of this 2D contour match to find the missing 3Dparameters that should be associated with them. In contrast, thepresently disclosed discriminative approach learns a direct mapping from2D image features in a single image to 3D shape and pose parameters.

For discriminative pose and shape estimation as depicted in FIG. 6, aMixture of Experts model 606 is employed, with experts defined usingkernel linear regression. A statistical learning method illustrated atblock 602 uses a database 601 of training body shapes, poses andcorresponding shape features to build a direct probabilistic mappingbetween monocular silhouette contour features and the body shape andpose parameters (in the form of the Mixture of Experts model 606). Theapproach recovers an approximation to the 3D shape and pose of the humanbody directly from features in a sensor data 603 such as a singlemonocular image. The input sensor data is processed to identify theforeground region corresponding to the body as illustrated by foregroundextraction block 604 and the result is then processed to extract shapefeatures as illustrated at block 605. Samples are drawn from thisprobabilistic model as illustrated at 609 where each sample correspondsto a 3D body pose 611 and shape 610. The sampled shapes are sufficientlyaccurate to initialize the more precise generative optimization processdiscussed in Section 6.

In one embodiment, the shape features in the database 601 are obtainedby projecting the example 3D body models model into the image plane of asynthetic camera to produce a silhouette. From this silhouette featuressuch as radial distance 608 or shape contexts 607 are estimated. Themixture of experts 606 is trained using the database 601 of body shapesand poses along with their corresponding shape features as projectedonto a synthetic camera view. Any suitable parametric model of the bodycould be used but in one embodiment, the SCAPE model is used to generate3D body shapes and their projected image silhouettes. While the focushere is on 2D image features, one should note that the learned mixtureof experts does not take images or silhouettes as input. In general, ittakes feature descriptors computed from sensor input. One can replacethe 2D silhouettes with range maps or other sensor data and computedifferent feature vectors such as 3D radial distance, sphericalharmonics, 3D curvature features, etc. In the case of a range sensor,the 3D body model is used to produce synthetic training range datacorresponding to particular sensor viewing directions. The core learningand prediction methods are independent of the source of the featurevectors. Furthermore, the sensor data may come from one or more sensorssuch as multiple camera views. In the case of multiple views, thefeatures associated with each view may be concatenated into one featurevector for training.

2D Shape Feature Extraction

The foreground extraction component 604 is used to extract a putativeregion corresponding to the location of the person in a 2D image. Imagesilhouettes are commonly used for human pose estimation; while limitedin their representational power, they are easy to estimate from imagesand fast to synthesize from a mesh model. Given a foreground region,shape feature descriptors are extracted to characterize the 2D shape605. They may be used together as a combined feature or separately. Twoshape features are described below but many other 2D image featurescould be used (e.g. shape context over internal and external edges(Sminchisescu et al. 2005) or descriptors such as SIFT (Lowe 2004), HOG(Dalal and Triggs 2005), Vocabulary Trees (Kanaujia et al. 2007),Hyperfeatures (Kanaujia et al. 2007) or HMAX features (Riesenhuber andPoggio 1999; Kanaujia et al. 2007)).

Feature 1: Histograms of shape context 607. Shape contexts (SC)(Belongie et al. 2001) are rich descriptors based on the localshape-based histograms of the contour points sampled from the boundaryof the silhouette (or internal and/or external edges). At every sampledboundary point the shape context descriptor is parameterized by thenumber of orientation bins, φ, number of radial-distance bins, r, andthe minimum and maximum radial distances denoted by r_(in) and r_(out)respectively. As in (Agarwal and Triggs 2006), scale invariance isachieved by making r_(out) a function of the overall silhouette heightand by normalizing the individual shape context histogram by the sumover all histogram bins. Assuming that N contour points are chosen (e.g.at random) to encode the silhouette, the full feature vector can berepresented using a histogram with r_(N) bins. Even for moderate valuesof N this produces high dimensional feature vectors that are hard todeal with.

To reduce the silhouette representation to a more manageable size, asecondary histogram step is used (Agarwal and Triggs 2006). In thisbag-of-words model, the shape context space is vector quantized into aset of K clusters (a.k.a. codewords). The K=100 codebook is learned byrunning k-means clustering on the combined set of shape context vectorsobtained from the large set of training silhouettes. Once the codebookis learned, the quantized K-dimensional histograms are obtained byvoting into the histogram bins corresponding to codebook entries. Softvoting has been shown (Agarwal and Triggs 2006) to reduce effects ofspatial quantization. The final descriptor X_(sc) of length K isnormalized to have unit norm to ensure that silhouettes that containdifferent number of contour points can be compared.

The resulting codebook shape context representation is translation andscale invariant by definition. Following prior work (Agarwal and Triggs2006; Poppe and Poel 2006) one embodiment uses φ=12, r=5, r_(in)=3, andr_(out)=κh where h is the height of the silhouette and κ is typically ¼,ensuring the integration of contour points over regions roughlyapproximating the size of a human limb (Agarwal and Triggs 2006); otherparameters settings are possible. For shape estimation, it has beendetermined that combining shape context features across multiple spatialscales (e.g. κ={¼, ½, . . . }) into a single feature vector is moreeffective. This can be done by simply concatenating the featurerepresentations obtained with different settings for κ. Since this mayresult in high dimensional feature vectors one can optionally performiterative feature selection (Bo et al. 2008) using one of a variety ofmachine learning techniques (e.g. by looking at the relative informationgain of each feature vector dimension).

Feature 2: Radial distance function 608. The Radial Distance Function(RDF) features are defined by a feature vector

X _(RDF) ={p _(c) , ∥p ₁ −p _(c) ∥, ∥p ₂ −p _(c) ∥, . . . , ∥p _(N) −p_(c)∥},

where p_(c) is a vector of image positions for the centroid of the imagesilhouette, and p_(i) is a point on the silhouette contour; hence∥p_(i)−p_(c)∥ is a scalar value measuring the distance from the centroidto point i on the contour. In one embodiment, we use N=100 points,resulting in the X_(RDF) being a vector of 102 elements. This ensuresthat the dimensionality of the RDF descriptor is comparable to that ofshape context feature above.

Unlike the shape context descriptor, the RDF feature vector is neitherscale nor translation invariant. Hence, RDF features are best suited forapplications where camera calibration is known and the training data canbe constructed using this known calibration information. This ispossible in an embodiment such as a changing room scanner where thecamera or other sensors remain in a fixed location and the location ofthe person is fairly constrained.

Mixture of Experts (Learning)

To produce initial estimates for the body pose and/or shape in 3D fromimage features, the present method first models the conditionaldistribution p(Y|X) of the 3D body state Y given the feature vector X.Intuitively this conditional mapping should be related to the inverse ofthe camera projection matrix and, as with many inverse problems, ishighly ambiguous. To model this non-linear relationship a Mixtures ofExperts (MoE) model is used to represent the conditional distribution(Agarwal and Triggs 2005; Sminchisescu et al. 2005).

The parameters of the MoE model are learned by maximizing thelog-likelihood of the training data set D={(x⁽¹⁾, y⁽¹⁾), . . . ,(x^((N)), y^((N)))} consisting of N input-output pairs (x^((i)),y^((i))). In one embodiment, an iterative Expectation Maximization (EM)algorithm, based on type-II maximum likelihood, is used to learnparameters of the MoE (Sminchisescu et al. 2005). The presentlydisclosed model for the conditional probability can be written as:

${p\left( {YX} \right)} \propto {\sum\limits_{k = 1}^{M}{{p_{e,k}\left( {{YX},\Theta_{e,k}} \right)}{p_{g,k}\left( {{kX},\Theta_{g,k}} \right)}}}$

where p_(e,k) is the probability of choosing pose Y given the input Xaccording to the k-th expert, and p_(g,k) is a “gate” that models theprobability of the input being assigned to the k-th expert using aninput sensitive gating network; in both cases Θ represents theparameters of the mixture and gate distributions respectively.

For simplicity and to reduce complexity of the experts kernel linearregression with constant offset, Y=βX+α, was chosen as the expert model,which allows an analytic solution of the parameters Θ_(e,k)={β_(k),α_(k), Λ_(k)} using weighted linear regression, where

${p_{e,k}\left( {{YX},\Theta_{e,k}} \right)} = {\frac{1}{\sqrt{\left( {2\; \pi} \right)^{n}{\Lambda_{k}}}}^{{- \frac{1}{2}}\Delta_{k}^{T}\Lambda_{k}^{- 1}\Delta_{k}}}$

and Δ_(k)=Y−β_(k)X−α_(k)=Y−μ_(k). Of course non-linear kernels (e.g.,Radial Basis Functions) could also be used and there are standardmethods to fit these to the data described herein.

Pose and shape estimation is a high dimensional and ill-conditionedproblem, so simple least squares estimation of the linear regressionmatrix parameters typically produces severe over-fitting and poorgeneralization. To reduce this, ridge regression is used and smoothnessconstraints are added on the learned mapping that regularize thesolution. The matrix of regression coefficients can be estimated asfollows:

β_(k)=(D _(Y) ^(T) W _(k) D _(Y) +λI)⁻¹ D _(Y) ^(T) W _(k) D _(X)

where D_(X)={x^((i))∥i=1 . . . N} is a vector of inputs,D_(y)={y^((i))|i=1 . . . N} is vector of corresponding outputs,W_(k)=diag(w_(k) ⁽¹⁾, w_(k) ⁽²⁾, . . . , w_(k) ^((N))) is a diagonalmatrix with optional “relative importance” parameters (for a givenexpert k), for each corresponding training sample, along its diagonal(w_(k) ^((i)) is between 0 to 1, such that sum over w_(k) ^((i)) for allk equals 1), I is the identity matrix, and λ is a smoothness parameter.The offset parameters α_(k) are estimated as

$\alpha_{k} = {\frac{\sum\limits_{i = 1}^{N}\; {w^{(i)}x^{(i)}}}{\sum\limits_{j = 1}^{N}w^{(j)}}.}$

Since the solution of the ridge regressors is not symmetric under thescaling of the inputs, the inputs {x⁽¹⁾, x⁽²⁾, . . . , x^((N))} arenormalized by the standard deviation in each dimension respectivelybefore solving.

The smoothness is controlled by a parameter λ. An overly smooth mapping(that results from setting λ to a large value) will not capture thestructure of the regression problem and will generally result in nearlythe same output pose and shape for any set of input features (renderingthe discriminative method useless). An under-smoothed mapping (resultingfrom setting λ to a very small value) will generally overfit thetraining data and also produce sub-optimal estimates on the test data.To choose an appropriate value for λ a withheld validation dataset isused to ensure that optimal performance is achieved.

To learn the gate parameters, the probability that a given trainingsample is generated by one of the M experts (e.g., by expert k) is firstestimated. This value, z_(k) ^((n)), is the “ownership weight” forexpert k of the training instance n. These ownership weights arecomputed by taking the product of the probability of activation of thegate for expert k (given an estimate of current gate parameters,Θ_(g,k))

${{p_{g,k}\left( {{{kX} = x^{(n)}},\Theta_{g,k}} \right)} = {\frac{1}{\sqrt{\left( {2\; \pi} \right)^{n}{\sum\limits_{k}}}}^{{- \frac{1}{2}}{({x - \mu_{k}})}^{T}{\sum\limits_{k}^{- 1}{({x - \mu_{k}})}}}}},$

and the probability of the expert k generating the desired output (giventhe estimate of the current expert parameters, Θ_(g,k)),

${p_{e,k}\left( {{Y = {{y^{(n)}X} = x^{(n)}}},\Theta_{e,k}} \right)} = {\frac{1}{\sqrt{\left( {2\; \pi} \right)^{n}{\Lambda_{k}}}}^{{- \frac{1}{2}}\Delta_{k}^{T}\Lambda_{k}^{- 1}\Delta_{k}}}$

divided by the sum of this product over all M experts:

$z_{k}^{(n)} = {\frac{{p_{e,k}\left( {{y^{(n)}x^{(n)}},\Theta_{e,k}} \right)}{p_{g,k}\left( {{kx^{(n)}},\Theta_{g,k}} \right)}}{\sum\limits_{j = 1}^{M}{{p_{e,j}\left( {{y^{(n)}x^{(n)}},\Theta_{e,j}} \right)}{p_{g,j}\left( {{jx^{(n)}},\Theta_{g,j}} \right)}}}.}$

Intuitively this measures the fraction of the time a desired output poseand shape is generated from a given input set of features by a givenexpert k. Once this is computed the new parameters of the gates can befound by computing sufficient statistics of the correspondingstatistical distribution, by weighting the input features by theprobability of them being interpreted by the given expert k; similarlythe parameters of the experts can be found by weighted regression basedon the input-output training pairs (with the same weights); see above.In the weighted regression the method simply uses “ownership weights”,z_(k) ^((i)), as “relative importance” weights, w_(k) ^((i)),”,resulting in W_(k)=diag(z_(k) ⁽¹⁾, z_(k) ⁽²⁾, . . . , z_(k) ^((N))). Theentire process can then be iterated to refine the parameters of themodel.

The above discussion describes the expectation-maximization (EM)procedure for the MoE model. In one embodiment, three separate modelsare learned: shape, p(ν|x), articulated pose, p(θ|X) and global positionof the body in the world, p(τ|X). Of course they could be combined andlearned together as well. Similar to (Agarwal and Triggs 2005) oneembodiment initializes the EM learning by clustering the output 3D posesand shapes using a k-means procedure. This results in z_(k) ^((i))=1 forthose training examples i that are assigned to the same k-th cluster,and z_(k) ^((j))=0 for all remaining samples.

Articulated pose and shape experiments were conducted using both RDF andSC features (global position requires RDF features since SC is locationand scale invariant). SC features tend to work better for poseestimation whereas RDF features perform better for shape estimation.Hence, the following conditional models are learned: p(ν|X_(RDF)),P(θ|X_(sc)) and p(ι|X_(RDF)). In cases where calibration is unavailable,the shape is estimated using p(ν|X_(SC)) which tends to producereasonable results but cannot estimate the overall height of the person.The number of mixture components, M, and regularization parameter, λ,are estimated by learning a number of models and cross validating on awithheld dataset.

Prediction/Sampling

Given the MoE model 606, initial guesses for the body shape and pose aregenerated given only a single input image or other sensor data. Inparticular, one embodiment does so by drawing samples from theprobabilistic model. Since the MoE defined above is a mixture of linearGaussian elements, this can be achieved given input feature vector X.Sampling involves first choosing an expert, k, at random, proportionalto the gaiting weights (which sum to one). This then defines a linearmodel that predicts the mean of the expert, μ_(k)=β_(k)X−α_(k). Finallya sample is drawn from the Gaussian distribution defined by p_(e,k).Since the model is divided up into separate discriminative models forthe shape, p(ν|X), position, p(τ|X), and articulated pose, p(θ|x), ofthe body, samples are drawn independently from each. To obtain a jointestimate for the pose, shape and position, the samples from the threemodels are combined. This can be done, for example, by independentlysampling from each of the three trained models and concatenating allparameters into a single joint sample vector. In general, this processmay require the total number of joint samples that is a product of thenumber of samples required to characterize each of the three conditionaldistributions.

Several such joint samples can be generated. These are then used tostart the optimization process using one of several methods to fit the3D body model to image or other sensor evidence (Section 6).Alternatively, the samples may be used without any further optimization.

Shape Consistency

The accuracy of this discriminative method can be improved by modelingthe consistency in the estimated shape over time. If several images ofthe person are available in possibly different poses, the shapeparameters θ should be consistent for all these poses. One can recover abetter set of shape parameters by taking a product over conditionaldistributions obtained in each frame. Since the form of each conditionaldistribution is a mixture of Gaussians, the final product will also be amixture of Gaussians, but the representation (and computation requiredto compute this final mixture) will grow exponentially with the numberof frames. One way to battle this computational complexity is bycharacterizing the modes of the distribution rather than the fulldistribution. This can be done by sampling an estimate for the shapeparameters from either one of the conditional distributions at random orfrom the product (e.g., by using Gibbs sampling (Ihler et al. 2003)) andthen refining this sample using a gradient ascent procedure defined overthe product of conditional distributions. This is efficient because thegradient of the product can be expressed using products of simplefactors from the gradient expressions of the individual conditionals.

Similarly, if it is known the poses come from a sequence of images thentemporal consistency may be enforced on the poses such that the changein pose between frames is small. This can be done by training anauxiliary discriminative model, p(θ_(t)|θ_(t−1), X_(t)), where thearticulated pose at frame t, θ_(t), is estimated (regressed) from thepose at the previous time frame t−1, θ_(t−1), and features at frame t,X_(t). In essence the training and the use of this model is preciselythe same as before, except the training proceeds to learn from datatriplets D={(θ_(t) ⁽¹⁾, θ_(t−1) ⁽¹⁾, x_(t) ⁽¹⁾), . . . , (θ_(t) ^((N)),θ_(t−1) ^((N)), x_(t) ^((N)))} (two inputs and a single output, θ_(t)).The pose estimation can then be done by using the old discriminativemodel, p(θ₁|X₁), for the first frame resulting in a distribution overθ₁; then subsequently using the auxiliary model, p(θ_(t)|θ_(t−1),X_(t)), to propagate these estimates temporally (while still taking intoaccount observations), e.g., p(θ₂|θ₁, X₂), p(θ₃|θ₂, X₃) and so on.

The key challenge is to ensure that the representation of distributionsover the articulated pose (θ) does not grow during inference as they arepropagated through this multi-modal conditional, p(θ_(t)|θ_(t−1),X_(t)), from frame to frame. This can be done by fitting a fixedrepresentation to the estimated distribution at every frame. For exampleby minimizing the KL divergence between a Gaussian mixture with a fixednumber of components and the estimated mixture (the number of componentsof which may differ from frame to frame).

4d. Initialization of Shape from User Supplied Measurements

Note that while the body shape estimation methods disclosed here provideone way of obtaining a body shape model, they are not the only way.Several on-line retail-clothing applications allow people to enter theirown body measurements; these are often quite inaccurate and variable.Still others allow users to answer various questions about what sizesfit them and their qualitative shape. Either of these input methods canbe used to match people to body shape models.

Nearest-Neighbor Matching

Referring to FIG. 7, in an off-line process a database 701 of 3D bodyshape models is generated using the capture methods described here orother methods such as 3D laser range scanning. Measurements andqualitative shape information are stored in the database for eachscanned subject. This is then used in a user-generated shape estimationcomponent. For a new person, their measurements and qualitative shapeinformation 702 is matched to the database 701 via a matching function703 to find similar people 704. From a selection or combination ofsimilar people 705, a body shape model 706 is constructed, for exampleby averaging the body shapes. Alternatively a plurality of matching bodyshapes are presented to the user on a display and they can select whichlooks most like them using a computer interface. This user-derived bodyshape can then be used for initialization or, without furtheroptimization, as any other body shape model.

The matching component 703 can be efficiently implemented as nearestneighbor search (NN) using any of several standard methods for efficientimplementation (e.g. using a KD-tree). One must be careful in defininghow measurements are matched and how this match is scored. Somemeasurements may be more reliable or more important than others andshould therefore count more heavily. One can select the best match andsimply take the body shape parameters of the corresponding person asthose of the user. Alternatively, the best n matches 704 can be takenand combined. Given a match score for each of the n matches, a weightedaverage of the shape coefficients for each matched body is computed. Theresulting set of linear shape coefficients is taken to represent theuser body.

Prediction Using Linear Regression

An alternative method is described by Allen et al (2003, 2004). Theapproach is to learn a mapping

body shape=f(measurements)

that expresses the shape coefficients β_(i) for a body i as a linearcombination of h body measurements m_(i) plus a bias constant

$\beta_{i} = {\begin{bmatrix}\beta_{1,i} \\\beta_{2,i} \\\vdots \\\beta_{k,i}\end{bmatrix} = {{F\begin{bmatrix}m_{1,i} \\m_{2,i} \\\vdots \\m_{h,i} \\1\end{bmatrix}} = {F\; m_{i}}}}$

Given a training set of n body shapes with measurements M andcorresponding shape coefficients B the constraints in matrix form as

$B = {\begin{bmatrix}\beta_{1,1} & \beta_{1,2} & \ldots & \beta_{1,n} \\\beta_{2,1} & \beta_{2,2} & \ldots & \beta_{2,n} \\\vdots & \vdots & \; & \vdots \\\beta_{k,1} & \beta_{k,2} & \ldots & \beta_{k,n}\end{bmatrix} = {{F\begin{bmatrix}m_{1,1} & m_{1,2} & \ldots & m_{1,n} \\m_{2,1} & m_{2,2} & \ldots & m_{2,n} \\\vdots & \vdots & \; & \vdots \\m_{h,1} & m_{h,2} & \ldots & m_{h,n} \\1 & 1 & \ldots & 1\end{bmatrix}} = {F\; M}}}$

Allen et al. (2003, 2004) learned F via least squares estimation

F=BM ^(†) =B(M ^(T) M)⁻¹ M ^(T)

where M^(†)is the pseudo-inverse of M.

It has been found that hand measurements are often inaccurate and leastsquares estimation is highly sensitive to outliers. Consequently thepresent invention uses a robust iteratively reweighted least squaresmethod to fit F.

For a practical method of initialization or body shape generation, it isimportant to 1) minimize the number of measurements that must be enteredand 2) maximize the contribution of each measurement. The internationalISO 20685 standard defines a comprehensive set of body measurements. Anoptimal subset of these or similar measurements is sought that predictsbody shape accurately. A greedy algorithm is defined to establish thissubset.

This algorithm is defined in detail in Section 10 for producing a set ofmultiple measurements from the body vertices. That method is a generalway of finding a set of predictors that predict multiple values. Herethe predictors are measurements, m_(i) (instead of vertices) and themultiple predicted values are linear shape coefficients.

With this greedy algorithm it has been determined that approximately 15measurements are sufficient to predict body shape with reasonableaccuracy.

SECTION 5. GENERIC OBJECTIVE FUNCTIONS

The presently disclosed model is parameterized by a set of poseparameters θ, shape coefficients β and gender χ. The problem ofestimating human body shape from sensor data is reduced to one ofsolving for the optimal body model parameters that minimize some errorfunction E(χ, β^(χ), θ) given sensor measurements. A generative approachis adopted in which predicted model parameters are used to construct a3D body model from which various features are extracted and comparedwith features from sensor data. Several error functions are describeddepending on the type of sensor input used: foreground image silhouettesfrom one or more calibrated camera views, or range images. Standardmethods are presented which are used to illustrate the fitting process.Additionally, methods are described to deal with more challengingsituations involving clothing or moving cameras.

5a. Camera Images

An initial embodiment is first described that uses calibrated foregroundimage silhouettes for estimating the body pose and shape parameters andassumes the subject wears minimal or tight fitting clothing. Balan etal. (2007a) used this approach to estimate body shape from multiplecalibrated cameras. The framework is general however and can beaugmented to exploit additional image features such as edges and opticalflow (Sminchisescu and Triggs, 2003), shadows (Balan et al. 2007b), etc.

Given an estimated body model reconstructed from the model parameters,the model is projected into a camera view k assuming known extrinsic andintrinsic camera calibration. This produces a predicted image silhouetteS_(k,χ,β) _(χ) _(,θ) ^(e). This silhouette is compared with the observedsilhouette, S_(k) ^(o), in camera view k, obtained by foregroundsegmentation (Section 2a).

Measures have been proposed in the literature for computing(dis)similarity of silhouettes. For instance, one of the most widelyused measures is based on silhouette overlap, computed by summing thenon-zero pixels resulting from a pixel-wise XOR between the two imagemasks (predicted and observed). While computationally efficient, thismeasure is not very informative in guiding the search duringoptimization. Instead a modified version of the Chamfer distance isemployed.

Specifically the asymmetric distance between silhouettes S and T isdefined as

${{{\overset{\sim}{d}}^{\tau}\left( {S,T} \right)} = \frac{\sum\limits_{i,j}\; {S_{ij} \cdot {C_{ij}^{\tau}(T)}}}{\sum\limits_{i,j}\; S_{ij}}},$

where S_(ij)=1 for the pixels inside silhouette S and 0 otherwise;C_(ij) ^(τ)(T) is a distance transform function which is zero if pixel(i,j) is inside T and is a robust Euclidean distance to the closestpoint on the boundary of T for points outside. In order to cope witherrors in the image silhouettes, C_(ij) ^(τ)(T) is made robust bycapping the Euclidean distance at a certain threshold τ (e.g. 20 pixelsfor an image size of 800 by 600). For pixels (i, j) that are more than τEuclidean distance away from T, C_(ij) ^(τ)(T)=τ. The denominator is anormalization term that gives invariance to the size of the silhouette.

The objective function for the minimal clothing case is first definedusing the bi-directional objective used by Balan et al. (2007a). This islater extended to deal with clothing. The objective function uses asymmetric distance to match the estimated and observed silhouettes for agiven camera view k

E _(1Pose;NoClothes;1Cam) ^(k)(χ,β^(χ),θ)={tilde over (d)} ^(τ)(S_(k,χ,β) _(χ) _(,θ) ^(e) ,S _(k) ^(o))+{tilde over (d)} ^(τ)(S _(k) ^(o),S _(k,χ,β) _(χ) _(,θ)).

In effect this objective function equally penalizes the regions of themodel silhouette that fall outside the image silhouette and the regionsof the image silhouette that are not covered by the model's projection.This is appropriate for the case where the subject wears tight-fittingclothing.

In the case where multiple synchronized camera views are used, where theimages are taken at the same time instant, the constraints over the Kcamera views are integrated to optimize a consistent set of modelparameters

${E_{{1\; {Pose}};{NoClothes}}\left( {\chi,\beta^{\chi},\theta} \right)} = {\sum\limits_{k = 1}^{K}{{E_{{1\; {Pose}};{NoClothes};{1\; {Cam}}}^{k}\left( {\chi,\beta^{\chi},\theta} \right)}.}}$

5b. Range Images

In contrast to image observations that provide constraints in 2D, thereexist sensors that capture depth measurements directly in 3D (e.g.sparse or dense stereo images, laser range scans, structured lightscans, time-of-flight sensors). Having 3D measurements simplifies thematching problem with a 3D body model. These measurements may consist ofpoint clouds or polygonal meshes, and optionally contain colorinformation or surface orientation.

One embodiment fits body pose and shape to this data using an IterativeClosest Point (ICP) strategy. Generic ICP is a well understood algorithmused for aligning two point clouds. Broadly speaking, the algorithmestablishes point correspondences between the source shape (body model)and the target shape (3D sensor measurements), defines an error functionthat encourages established corresponding points to be aligned, computesthe optimal parameters that minimize the error, transforms the sourceshape using the optimal parameters and iterates to establish new pointcorrespondences and refine the alignment.

One embodiment uses the error term E_(1Pose,NoClothes,3D) (χ,β^(χ),θ) toencourage the vertices y_(v) on the body model to move towards theclosest respective points on the target shape T given by the sensordata:

${E_{{1\; {Pose}};{NoClothes};{3\; D}}\left( {\chi,\beta^{\chi},\theta} \right)} = {\sum\limits_{v \in V}\; {w_{v}{{\Gamma_{\tau_{dist}}^{2}\left( {{y_{v}\left( {\chi,\beta^{\chi},\theta} \right)},T} \right)}.}}}$

Here V denotes the set of body model vertices and the function Γ_(τ)_(dist) (y_(v),T) computes the distance from a vertex y_(v) to theclosest compatible point on the target shape T. Note that the closestcompatible point is selected only at the beginning of each ICP iterationand this correspondence is maintained during the optimization of bodymodel parameters. From an implementation point of view, a KD-treestructure is used to efficiently establish correspondences with thetarget shape. The compatibility criterion restricts the distance betweenthem to a threshold τ_(dist), (e.g. 150 mm) to avoid matching throughholes in the target shape. In the case where the target shape isrepresented as a mesh or an oriented point cloud, the compatibilitycriterion also safeguards against front-facing surfaces being matched toback-facing surfaces, measured in terms of the angle between the surfacenormals. Two points are considered incompatible if their normals aresignificantly apart (typically by more than 45 degrees). If there are nocompatible points for a vertex, the Γ distance is simply set to zero.The weight w_(v) is used to account for holes in the target shape,particularly in the case of partial scans or depth maps that onlyprovide a partial view of the body shape. In this case many vertices onthe body model have no correct correspondence on the scanned mesh.Fortunately, at each ICP iteration, the vertices y_(v) with no truecorrespondence can readily be identified as the ones whose closest pointon the target shape is located on the boundary edge of a hole. For thesevertices the weight w_(v) is set to 0; in all other cases w_(v) is equalto 1. Moreover, for calibrated sensing devices that only provide a rangeimage for half the object (i.e. the part visible to the sensor), at eachICP iteration vertices on the current model that could not have be seenby the sensing device given the current estimate of the body areidentified and their w_(v) weights are set to 0.

SECTION 6. OPTIMIZATION

Two types of penalty functions are identified that are used to recoverthe parameters of interest (i.e. body shape and pose): 1) sensor errorterms E_(sensor)(χ, β^(β), θ, . . . ) that penalize mismatches betweenthe estimated model and the input sensor data, and 2) prior error termsE_(prior)(χ, β^(β), θ, . . . ) that enforce domain knowledge about themodel parameters. The latter type are described in Section 6b. It shouldbe understood that the sensor error terms can be linearly combined (thuschanging the relative importance of each term) together with the priorenergy terms to obtain a global objective function that we seek tooptimize:

E(χ,β^(χ),θ, . . . )=E _(sensor)(χ,β^(χ),θ, . . . )+E_(prior)(χ,β^(χ),θ, . . . )

Example sensor error terms include E_(1Pose;NoClothes;1Cam) ^(k),E_(1Pose;NoClothes), E_(1Pose;NoClothes;3D) (Secton 5),E_(clothes;2D;sensor), E_(clothes;3D;sensor) (Section 7), E_(Sequence)(Section 8). Section 6b defines the following prior error terms:E_(constraints), E_(shape), E_(pose) and E_(interpenetration).

Robust Penalty Functions

In the sensor and prior error terms described below there is often apenalty function, denoted ρ(□). Although this can be as simple asρ(x)=x², in many cases it is beneficial to use a robust penaltyfunction. Many robust penalty functions may be used including L1, Hubermini-max, Lorentzian, Tukey's bi-weight, etc. (see Black and Rangarjan1996 for examples). In one embodiment the robust penalty function is theGeman-McClure function

${\rho (x)} = {\frac{x^{2}}{\sigma^{2} + x^{2}}.}$

6a. Optimization Strategy

A series of objective functions of the form E(χ, β^(χ), θ, . . . ) aredefined and minimized to recover shape and pose. Since the number ofparameters to estimate is large and the objective function has localoptima, several strategies are described that can be used to effectivelyfind good solutions.

First, initial estimates of the parameters are optionally obtained usingthe techniques described in Section 4, which provide a good startingpoint for optimization. An optional stochastic search method (Balan etal. 2007a) can be used to generate more hypotheses of possible shape andpose parameters. Initial estimates of pose and shape are then refinedusing a direct search method. In particular, the simplex methoddescribed by Lagarias et al. (1998), a gradient-free direct searchmethod, may be used; in one embodiment this is implemented using theMATLAB function “fminsearch” (MATLAB 2008). Alternatively, any othersuitable optimization technique can be applied.

Gender and Subpopulation Estimation

In many applications, the gender of a person being scanned may be knownor the user may specify that information. In these cases, body shapeusing the appropriate gender-specific body model is estimated (Section3). When gender is not known there are several options. One can fit agender-neutral body model that is capable of representing male or femalebodies. Second, one can fit using both male and female body shape modelsand select the one that achieves a lower error of the objectivefunction. Third, one can fit a gender-neutral model and then classifygender directly from the estimated shape coefficients, as described inSection 10. Once gender is known, a refined shape estimate using theappropriate gender-specific shape model is produced. The same strategiescan be used for other subpopulations (e.g. to infer ethnicity).

Partitioned Search Space

Faster convergence is obtained by partitioning the search space. For agiven frame and gender value, in one embodiment it is desirable toalternate between optimizing pose and optimizing shape in an incrementalfashion: after initializing with an initial pose and shape model, theprocess of optimizing the global position of the torso and the first fewshape coefficients (e.g. the first 6) corresponding to the shapevariation directions with the largest eigenvalues is commenced. Therotation of individual body parts is then estimated, starting with thoseclosest to the torso (upper arms and upper legs) followed by lower armsand legs. Then all part rotations together with additional shapecoefficients (e.g. the first 12) are jointly optimized. In the lastphase, the full set of unknown variables including all part rotationsand shape coefficients are optimized.

In the case where integration of information across multiple poses isperformed, the optimization process alternates between optimizing asingle set of shape parameters applicable to all postures, andoptimizing the pose parameters θ_(p) independently for each posture.

Coarse-to-Fine

A computational speedup can be achieved by adopting a coarse-to-fineapproach where the body model is fit to a low-resolution image and theparameters are refined at successively finer resolutions in a standardmulti-resolution image pyramid.

6b. Constrained Optimization

Sensor evidence is often noisy or ambiguous, for example in the case ofone, or a small number of, images, or a single low-resolution rangeimage. In cases like these it can be difficult or impossible toaccurately estimate pose and shape without some sort of prior knowledge.With the application of appropriately formulated priors and constraintsin the optimization process, model fitting can be greatly improved.

There are two classes of prior knowledge that are used to constrain theoptimization process: knowledge about the specific individual, such asheight, weight, age, or gender; and knowledge that applies to allhumans. The former must be formulated in such a way that all theavailable information about the individual can be used effectively. Twoapproaches to this problem are described, each having differentadvantages and areas of applicability: hard constraints, where thesearch space of the optimization is limited to those values that satisfythe constraints; and soft constraints where the search space is notrestricted but rather deviations from the constraints are penalized inthe optimized energy function.

1. Hard Constraints on Body Shape

It is desirable to constrain body shape to maintain certain attributes;in particular, the case is considered in which there is a strong linearrelationship between said attributes and the shape coefficients (e.g.height). In general, if the shape is represented as a k-dimensionalvector β=[β₁, . . . , β_(k)]^(T), the set of all possible shapes isgiven by R^(k). However, a set of h, where h<k, attributes, which areconstrained to fixed values m=[m₁, . . . , m_(h)]^(T), defines a linearsubspace of R^(k) in which those constraints are satisfied. Optimizationcan be performed such that the shape varies only in this sub-space.

For each attribute iε{1, . . . , h} the axis {right arrow over (d)}_(i)is found in the shape space R^(k) that is the direction of maximumchange (typically called the attribute axis). This axis is simply thegradient of the attribute with respect to the shape parameters

${\overset{->}{d}}_{i} = {{\nabla m_{i}} = \left\lbrack {\frac{\partial m_{i}}{\partial\beta_{1}},\frac{\partial m_{i}}{\partial\beta_{2}},\ldots \mspace{14mu},\frac{\partial m_{i}}{\partial\beta_{k}}} \right\rbrack}$

and can be computed empirically from training data. To the extent thatvariation in body shape is linear in the constraining attribute, anychange in shape orthogonal to the attribute axis does not alter theattribute value. Therefore the subspace of all feasible solutions isgiven by the k−1 dimensional hyperplane orthogonal to {right arrow over(d)}_(i) and containing a shape point that achieves the desiredattribute value m_(i). Since there are h attribute constraints, thespace of all valid solutions is given by the intersection of h k−1dimensional hyperplanes. Assuming the attribute axes are linearlyindependent, the intersection is the k−h dimensional hyperplane thatcontains a point satisfying all the constraints and is the orthogonalcomplement to the subspace of R^(k) spanned by the attribute axesD=[{right arrow over (d)}₁, . . . , {right arrow over (d)}_(h)]. Theorthogonal complement for D is given by W=[{right arrow over (w)}₁, . .. , {right arrow over (w)}_(k−h)]=null(D^(T)). In order to find a pointof intersection of the hyperplanes, the strategy presented in Section 4dis used to learn a direct mapping F from attribute values m to a shapeβ⁰ satisfying the attribute constraints:

$\beta^{0} = {{F\begin{bmatrix}m \\1\end{bmatrix}}.}$

This point together with the orthogonal complement of the space spannedby the attribute axes fully determine the attribute preserving subspace.The shape β=[β₁, . . . , β_(k)]^(T) is therefore re-parameterized interms of hyper-parameters β′=[β₁′, . . . , β_(k−h)′]^(T) as

${\beta \left( \beta^{\prime} \right)} = {{W\; \beta^{\prime}} + {{F\begin{bmatrix}m \\1\end{bmatrix}}.}}$

This method has the advantage of speeding up optimization, for alloptimization methods, because it reduces the search space. It requiresthat body shape be linear in some function of the constraints, but wefind that for many useful constraints this is sufficiently close totrue. For example, body shape is sufficiently linear in height and cuberoot of weight.

2. Soft Constraints on Body Shape

Often user-supplied attributes, such as height or weight, are known.Solutions (body shapes) are preferred that agree with these attributes.Constraining body shape to match certain attributes is enabled by theattribute estimation method in Section 10, which predicts attributesfrom shape parameters β. Human measurements are noise prone and may bebiased; other properties may be discrete (clothing size or self reportedfrequency of exercise). In these cases user constraints are enforcedonly weakly.

Given a function predicting measurements from body shape, a prior isdefined that combines multiple “soft” constraints and this prior isincluded in the overall objective function. Specifically,

${E_{constraints}(\beta)} = {\sum\limits_{i = 1}^{h}{w_{i}{\rho \left( {{f_{i}(\beta)} - m_{i}} \right)}}}$

is defined where there are h soft constraints corresponding to knownattribute values m_(i) and for each of them a function ƒ_(i)(β) is knownthat takes body shape parameters and predicts attributes (Section 10).The error function ρ can be either quadratic or a robust error functionand w_(i) is a scalar weight inversely related to the uncertainty ofattribute m_(i). The scalar weights can be estimated from training datafrom the residual variance in fitting ƒ_(i)(β).

The power of this method is in the flexibility in defining ƒ_(i)(β). Forstochastic and simplex optimization methods, this function could beanything (such as a non-parametric method using nearest-neighborsearch). In one embodiment we take ƒ_(i)(β) to be a linear function asdescribed in Section 10; this makes the constraint term differentiablewith respect to the shape parameters.

3. Other Prior Error Terms

The two above constraining methods are user-specific. Prior error termsthat apply to all bodies are described below.

Interpenetration. A priori it is known that the pose and shape cannot besuch that the body interpenetrates itself or known objects in a theworld; a plausible estimate can never, for example, have one of the armsinside the torso. Previous model-based methods for preventing thiscondition tend to use simplified part-based representations of bodyshape since, for general meshes, testing mesh intersection is anontrivial computation. The aligned nature of the presently disclosedparametric model is leveraged to approach the accuracy of a general meshbased interpenetration test while preserving the desirable computationalproperties of simpler models.

The presently disclosed model is already segmented into P individualbody parts; it is known which vertices of the model correspond to bodypart p (Section 3). One can approximate a test to determine if two bodyparts intersect by testing if any vertex of the first part is inside theconvex hull of the second part. This can be done using a standardpoint-in-polygon (PIP) test in 3D: if any dot product of the ray, goingfrom the point to each surface triangle center, with the triangle normal(where the triangles have been oriented such that their normals pointoutside) is negative, then the point cannot be in the convex polygon.The penalty function is then defined as

${E_{interpenetration}\left( {\chi,\beta^{\chi},\theta} \right)} = {\rho\left( {\sum\limits_{p = 1}^{P}{\sum\limits_{v \in {Y/Y_{p}}}{{PIP}\left( {v,{{convhull}\left( {Y_{p}\left( {\chi,\beta^{\chi},\theta} \right)} \right)}} \right)}}} \right)}$

which counts the number of mesh vertices v that are inside the convexhull of each of the body parts (excluding of course the verticesbelonging to the part itself). Y is used to denote the set of all meshvertices, Y_(p) the set of vertices belonging to part p, and ρ a robustoperator. In general, the torso is not well approximated by its convexhull and consequently a test is performed to determine if torso verticesare inside other body parts, but not vice-versa.

Another important case of interpenetration is between the body model andthe ground plane. In cases where the ground plane is known (e.g. as aresult of calibration), an additional interpenetration penalty is addedto penalize body shapes and poses that produce vertices that like belowthe ground. Testing for intersection with ground is straightforwardbecause it is assumed to be a plane. A high penalty can be used toprevent any interpenetration or the distance of the model below theground can be computed and the penalty can be a function of thisdistance. Analogously a penalty for “floating” above the ground ensuresthat the body model touches the ground plane.

Shape prior. A penalty is defined for body shapes that do not conform tothe observed statistics of true human bodies. The present body shapemodel is learned from training bodies (Section 3) and the resulting PCAmodel includes the variance along each principal component direction.The variance, σ_(β,i,χ), along these shape-deformation directionscharacterizes the shape of the population being modeled. A standardGaussian noise assumption would lead to an error term defined by theMahalanobis distance of a body from the mean.

To avoid biasing the estimates toward the mean one embodiment uses adifferent penalty term. Specifically, a robust shape prior is formulatedthat penalizes extreme shapes while assigning the same fixed cost formore average shapes:

${E_{shape}\left( {\chi,\beta^{\chi}} \right)} = {\sum\limits_{i}{\rho\left( {\max\left( {0,{\frac{\beta_{i}^{\chi}}{\sigma_{\beta,i,\chi}} - \sigma_{\beta}^{thresh}}} \right)} \right)}}$

where ρ is robust operator. Typically σ_(β) ^(thresh)=3, is chosen, thuspenalizing only those shapes that are more than 3 standard deviationsfrom the mean.Pose prior. There are some poses that are anatomically impossible orhighly unlikely. The elbow, for example, cannot extend beyond a certainangle. To control this, a prior is enforced on body pose that is uniformwithin joint angle limits and only penalizes poses beyond those limits.Impossible joint angles are penalized in a robust manner, similar informulation to the shape prior:

${E_{pose}(\theta)} = {{\sum\limits_{i}{\rho_{1}\left( \frac{\max \left( {0,{\theta_{i}^{\min} - \theta_{i}},{\theta_{i} - \theta_{i}^{\max}}} \right)}{\sigma_{\theta,i}} \right)}} + {w{\sum\limits_{i}{\rho_{2}\left( {\max\left( {0,{\frac{{\theta_{i} - \theta_{i}^{0}}}{\sigma_{\theta,i}} - \sigma_{\theta}^{thresh}}} \right)} \right)}}}}$

where i ranges over all the pose rotation parameters. Note that both theangle bounds [θ_(i) ^(min), θ_(i) ^(max)] and the variances σ_(θ,i) canbe specified from anthropometric studies or learned from motion capturedata. The second term penalizes poses that deviate more than σ_(θ)^(thresh) standard deviations (typically 3) from an initial p ose θ_(i)⁰. This second term is appropriate for cases when the initial pose ispre-specified and known, but varies between subjects or between imagesof the same subject. In such cases, w is set to 1; if the initial poseis unknown, w is set to 0.6c. Optimizing Shape Across Varying Pose

In many situations it is desirable to be able to estimate human shapeeven when there is limited information. Doing so may require combininginformation from multiple frames of sensor data. If these frames arecaptured at different time instants, the articulated body pose maychange between frames. Consequently the presently described system canoptimize a single consistent body shape across frames containingdifferent poses.

Case 1: Multiple monocular images with changes in pose between images.Consider the situation there are two or more digital images of a persontaken at different times. In the time between capturing each image theperson's pose may have changed. Each image on its own provides verylimited information about the shape. Consequently it would be desirableto combine information from multiple such images. A video sequence froma single camera (e.g. a surveillance camera or a movie or televisionshow) presents an equivalent scenario.Case 2: Clothing that obscures the body. Often it is desirable to knowthe shape of a person without having to have them undress or wear tightfitting clothing. Here any single pose of the body does not reveal theentire shape. This is true whether the sensor data is images or moredetailed 3D data (e.g. from a laser range scanner, time of flightsensor, or structured light system). Here it is noted that as a personmoves in their clothes, the way the clothes obscure the bodychanges—they become loose or tight on different parts of the body indifferent poses. By combining information from all these poses, and byusing what is known about the shape of human bodies, one can estimatethe most likely shape underneath the clothing.

In both cases, the presently disclosed approach relies on using a bodymodel that factors body shape from the pose representation. Indeed ithas been found that the SCAPE model provides a representation of bodyshape in terms of the shape coefficients β that is relatively invariantto body pose θ (Balan et al. 2008). To exploit this constancy, a “batch”optimization is defined that extends the objective function to include Pdifferent poses but a single body shape consistent for all poses:

${{E_{batch}\left( {\chi,\beta^{\chi},\Theta} \right)} = {\sum\limits_{p = 1}^{P}{E_{{{1{Pose}};}*}\left( {\chi,\beta^{\chi},\theta_{p}} \right)}}},$

where Θ=(θ₁, . . . , θ_(p)) and E_(1pose) represents an error term thatevaluates how well the pose and shape estimates match the sensorobservations at a single time instant (e.g. E_(1pose;NoClothes;1Cam)^(k), E_(1Pose;NoClothes), E_(1Pose;NoClothes;3D)). The particularchoice depends on the type of sensor data (images or depth sensors) asdescribed in Section 5.

SECTION 7. CLOTHING

Estimating the human shape is made more challenging when the subject iswearing loose clothing that obscures the true form of the naked body.The vast majority of existing methods for estimating human shape requirethat the subject undress or wear minimal tight fitting clothing andcannot cope with the case where the clothing obscures the body shape.Various sensing/scanning technologies exist that allow fairly directaccess to body shape under clothing including backscatter X-ray,infra-red cameras and millimeter waves. While the presently disclosedbody fitting techniques could be applied to these data, for manyapplications, such as forensic video analysis, body shape must beextracted from standard video images or range measurements. This problemis relatively unexplored.

Here an observation model is defined that deals with clothing robustlyusing the concept that silhouettes in 2D, and range data in 3D,represent bounds on the underlying body shape. Consequently the truebody should fit “inside” the image measurements. In the case of aclothed person, the observations may only provide loose bounds on bodyshape. This makes the problem significantly under-constrained andtherefore requires additional assumptions to regularize the solution;this is achieved using the error terms defined in Section 6.Additionally, the objective function is made aware of the clothing, orlack of it, in different regions of the body. Regions in the sensor dataare identified that are likely to be skin. In these regions, theoptimization method constrains the fitted body model to match the sensorobservations (silhouette contours or range data). In the remainingclothed (or hair) regions, the objective function is modified so that itdoes not have to strictly match the observations. Additionally, it isnoted that clothing provides constraints on body shape that vary withpose as illustrated in FIG. 8. In each posture depicted in FIG. 8, theclothing is loose or tight on different parts of the body. Each postureprovides different constraints on the possible underlying body shape.Constraints from multiple poses, such as these, are accumulated by aconsistent body model across poses as described in Section 6.

7a. Camera Images

In the case of image silhouettes, the concept is introduced of a maximalsilhouette-consistent parametric shape that weakly satisfies thefollowing constraints:

-   -   1. the projected model falls completely inside the foreground        silhouettes;    -   2. the model attempts to fill the image silhouette mainly in        regions with tight or no clothing;    -   3. the intrinsic shape is consistent across different poses; and    -   4. the shape of the object belongs to a parametric family of        shapes (in our case human bodies).        Each aspect is discussed below.

The first constraint is satisfied by penalizing the regions of theprojected model silhouette, S_(k,χ,β) _(χ) _(,θ), that fall outside theobserved foreground silhouette S_(k) ^(o). The silhouette match error incamera k from Section 5 is separated into two pieces:

E _(1Pose;clothes;2D;1Cam)(χ,β^(χ),θ)=E _(inside) ^(k)(χ,β^(χ),θ)+E_(expand*) ^(k)(χ,β^(χ),θ)

For the “inside” term, the same distance function as defined in Section5a is used:

E _(inside) ^(k)(χ,β^(χ),θ)={tilde over (d)} ^(τ)(S _(k,χ,β) _(χ) _(,θ),S _(k) ^(o)).

For the second constraint, it is desirable that the projected modelexplain as much of the foreground silhouette as possible; if the subjectwere not wearing clothing this would just be the second term from theminimal-clothing case: {tilde over (d)}^(τ)(S_(k) ^(o), S_(k,χ,β) _(χ)_(,θ) ^(e)). In the more general setting where people wear clothing orinteract with objects, the observed foreground silhouettes will be toolarge producing a bias in the shape estimates. To cope with this,several strategies are employed. The first is to down-weight thecontribution of the second constraint, meaning it is more important forthe estimated shape to project inside the image silhouette than to fullyexplain it. The second is to use features in the image that are morelikely to accurately conform to the underlying shape. In particular,skin-colored regions are detected and, for these regions, the secondconstraint is given full weight. The detected skin regions are denotedby S_(k) ^(s) and the non-skin regions of the observed foregroundsilhouette by S_(k) ^(o)\S_(k) ^(s). Third, in the non-skin regions arobust penalty function controlled by a parameter τ^(c)<τ is employed.Recall that the distance function, {tilde over (d)}^(τ), already has athreshold τ on the maximum distance, which makes the term robust tosegmentation errors. In putative clothing regions this threshold isreduced to τ^(C). When the clothes are tight (or skin is beingobserved), it is desired that the error term increasingly penalizenon-skin regions even when they are far from the model silhouette. Inthis case, a large threshold τ is appropriate. However, if the clothesare expected to be loose, a small threshold τ^(c) effectively disablesthe silhouette distance constraint in non-skin regions. It is possibleto apply the robust operator also to the skin term (with a correspondingτ^(s) threshold greater than τ^(c)) to protect against errors in skindetection (but typically τ^(s):=τ).

The “expansion” constraint is then written as

E _(expand) ^(k)(χ,β^(χ),θ)={tilde over (d)} ^(τ) ^(s) (S _(k) ^(s) ,S_(k,χ,β) _(χ) _(,θ))+λ_(c) {tilde over (d)} ^(τ) ^(c) (S _(k) ^(o) \S_(k) ^(s) ,S _(k,χ,β) _(χ) _(,θ) ^(e))

with λ_(c)□1 (e.g. 0.1).

Different parts of the body can be obscured by different pieces ofclothing with different looseness characteristics. The above formulationcan be extended to incorporate any additional knowledge about thelooseness of clothing in G different regions of the body. Moregenerally, imagine the image silhouette is segmented into regionscorresponding to different classes of clothing with associatedlooseness/tightness properties. Such classes can represent broadcategories such as skin versus non-skin regions as described above, orcan include more refined categories such as hair, t-shirt, jacket etc.Each category, g, has an associated looseness threshold τ_(g) andrelative importance λ_(g). The “expansion” constraint can be generalizedas:

${E_{{expand}\; 2}^{k}\left( {\chi,\beta^{\chi},\theta} \right)} = {\sum\limits_{g = 1}^{G}{\lambda_{g}{{{\overset{\sim}{d}}^{\tau^{g}}\left( {S_{k}^{g},S_{k,\chi,\beta^{\chi},\theta}^{e}} \right)}.}}}$

Segmentation of the image into G labeled regions can come from userinput or can be obtained automatically using general skin, clothing andhair classifiers described in the literature (see Section 2e).

When a clothed subject is observed with clothing in only a single pose,the shape estimate may not be very accurate. Additional constraints canbe obtained by observing the subject in different poses. This requiresestimating a different set of pose parameters in each frame, but asingle body shape consistent for every pose (Section 6c):

${E_{{clothes};{2D};{1\; {Cam}}}\left( {\chi,\beta^{\chi},\Theta} \right)} = {\sum\limits_{p = 1}^{P}{E_{{1{Pose}};{clothes};{2D};{1{Cam}}}^{k}\left( {\chi,\beta^{\chi},\theta_{p}} \right)}}$

where Θ=(θ₁, . . . , θ_(p)) represents the different body poses.

In the case of multiple synchronized camera views where the images aretaken at the same time instant, we integrate the constraints over the Kcamera views to optimize a consistent set of model parameters:

${E_{{clothes};{2D};{sensor}}\left( {\chi,\beta^{\chi},\Theta} \right)} = {\sum\limits_{k = 1}^{K}{E_{{clothes};{2D};{1{Cam}}}^{k}\left( {\chi,\beta^{\chi},\Theta} \right)}}$

Finally, the sensor constraints are combined with domain knowledgeconstraints to ensure the shape remains within the family of humanshapes by exploiting the availability of a large database of bodyshapes. It is not required that the estimated shape exist in thedatabase; instead, computed statistics on shape variability are used topenalize unlikely shape parameters, E_(shape) (β^(χ)) as described inSection 6b. Pose and interpenetration priors E_(pose)(θ_(p)) andE_(interpenetration) (χ, β^(χ), θ_(p)) that penalize un-natural posesexceeding anatomical joint angle limits are also enforced (alsodescribed in Section 6b). The final objective function is

${E_{{clothes};{2D}}\left( {\chi,\beta^{\chi},\Theta} \right)} = {{E_{{clothes};{2D};{sensor}}\left( {\chi,\beta^{\chi},\Theta} \right)} + {E_{shape}\left( {\chi,\beta^{\chi}} \right)} + {\sum\limits_{p = 1}^{P}{E_{pose}\left( \theta_{p} \right)}} + {\sum\limits_{p = 1}^{P}{E_{interpenetration}\left( {\chi,\beta^{\chi},\theta_{p}} \right)}}}$

This objective function is optimized using the strategy described inSection 6.

7b. Range Data

The concepts used for the camera images can be applied to the case of 3Dsensor measurements. The shape is sought that weakly satisfies thefollowing constraints:

-   -   1. the fitted model is close to the 3D measurements in regions        with tight or no clothing;    -   2. the 3D range measurements lie outside the body;    -   3. the intrinsic shape is consistent across different poses; and    -   4. the shape of the object belongs to a parametric family of        shapes (in our case human bodies).

Building on the approach presented in Section 5b, the optimization isformulated using a weighted Iterative Closest Point (wICP) algorithm.

First, tightness constraints are derived by identifying clothed andunclothed regions in the target shape T (i.e. the sensor rangemeasurements). The unclothed regions dominate the fitting process bydown-weighting the distance function for model vertices corresponding toclothed regions. Bare skin detectors are used to identify areas insensor data that provide tight constraints on shape (e.g. identify thearms and legs of a person wearing loose shorts and t-shirt).Specifically, in the case of range data that comes with associatedtexture information (e.g. a registered color image or a texture map),skin regions are detected similarly to the image case using acolor-based skin classifier (see Section 2e). These areas are used toguide the parametric shape and pose fitting process and rely on thecorrelations in the learned model of body shapes to provide the shapefor model regions that do not have tight constraints.

At a given ICP iteration, let V_(S) be the set of body model verticeswhose closest match on the target shape T was classified as skin, andV\V_(s) the non-skin vertices. For the skin regions, the same errorfunction is used as defined in Section 5b, fully enforcing the tightnessconstraint, while for the non-skin regions, their contribution isdown-weighted through λ_(c):

${E_{{1{Pose}},{Skin},{3D}}\left( {\chi,\beta^{X},\theta} \right)} = {{\sum\limits_{v \in V_{s}}{w_{v}{\Gamma_{\tau_{dist},\tau_{dist}^{s}}^{2}\left( {{y_{v}\left( {\chi,\beta^{\chi},\theta} \right)},T} \right)}}} + {\lambda_{c}{\sum\limits_{v \in {V\backslash V_{s}}}{w_{v}{\Gamma_{\tau_{dist},\tau_{dist}^{c}}^{2}\left( {{y_{v}\left( {\chi,\beta^{\chi},\theta} \right)},T} \right)}}}}}$

Recall from Section 5b that Γ is the distance from vertex y_(v) to theclosest compatible point on T, w_(v) is a binary variable that is 1 onlyfor visible vertices whose closest point on T is not on a hole boundary,and τ_(dist) prevents matches more than τ_(dist) distance away. If thesubject is wearing clothing, the target shape will be enlarged withoutnecessarily exceeding the τ_(dist) threshold (e.g. 150 mm), which isintended to prevent matching when there is no true correspondence due tolarge regions of missing data. As such, the range measurements inclothed regions will bias the shape estimates. For the non-skin regions,the Γ distance is made robust to clothing by capping the Euclideandistance at a threshold τ_(dist) ^(c). This parameter is the equivalentof τ^(c) in the image case (Section 7a). For vertices whose distance tothe closest compatible point on T is larger than τ_(dist) ^(c), Γ is setto τdist^(c). In the case of loose clothing, the τ_(dist) ^(c) parameteris set much lower than for non-skin regions, effectively disabling thetightness constraint unless the model is very close to the target shapeT. In the case of tight clothing, τ_(dist) ^(c) needs to be set larger.For the skin regions, an equivalent parameter τ_(dist) ^(s) can beintroduced with a larger value; typically τ_(dist) ^(s):=τ_(dist).

More generally, as in the image case, the target shape can be segmentedinto multiple regions V_(g) (with user input or automatically usinggeneral skin/hair/clothing classifiers described in the literature)corresponding to G classes of clothing with associated loosenessthresholds τ_(dist) ^(g) and relative importance λ_(g):

${E_{{1{Pose}},{Classes},{3D}}\left( {\chi, \beta^{\chi}, \theta} \right)} = {\sum\limits_{g = 1}^{G}{\lambda_{g} {\sum\limits_{v \in V_{g}}{w_{v} {\Gamma_{\tau_{dist},\tau_{dist}^{g}}^{2}\left( {{y_{v}\left( {\chi, \beta^{\chi}, \theta} \right)}, T} \right)}}}}}$

One undesirable property of this error term is that it treats the sourceshape and the target shape almost symmetrically. It fails to account forthe fact that clothing has a uni-directional effect; clothing increasesthe observed shape which means the body model should fit entirely insidethe target shape, but does not have to fully explain it. In the case ofpartial scans, the “inside” property is poorly defined. Rather, theconstraint is formulated that all points of the target shape must lieoutside or on the surface of the body model. In one embodiment, apenalty term is introduced to account for points that are inside thebody:

${E_{{1{Pose}},{Inside},{3D}}\left( {\chi,\beta^{\chi},\theta} \right)} = {\sum\limits_{v \in T}{\Lambda^{2}\left( {T_{v},{Y\left( {\chi,\beta^{\chi},\theta} \right)}} \right)}}$

The function Λ(T_(v),Y) computes the Euclidean distance by which atarget vertex T_(v) is inside the body mesh Y. Because the mesh isclosed, a standard Point-In-Polygon test (i.e. choose any ray throughthe point and count the number of intersections it makes with the meshY; if that number is odd then the point is inside Y) will determine ifthe point is inside Y. If not then the distance is set to 0. If thepoint is inside Y, Λ(T_(v),Y) is simply the distance from the pointT_(v) to the closest point on the mesh Y, capped at τ_(dist) to berobust against noise in the sensor data.

A full objective can be obtained by estimating a consistent shape acrossP different poses

${E_{{clothes};{3D};{sensor}}\left( {\chi,\beta^{\chi},\Theta} \right)} = {\sum\limits_{p = 1}^{P}\left( {{E_{{1{Pose}},{Classes},{3D}}\left( {\chi,\beta^{\chi},\theta_{p}} \right)} + {E_{{1{Pose}},{Inside},{3D}}\left( {\chi,\beta^{\chi},\theta_{p}} \right)}} \right)}$

and expanded to include domain knowledge constraints as described inSection 6:

${E_{{clothes};{3D}}\left( {\chi,\beta^{\chi},\Theta} \right)} = {{E_{{clothes};{3D};{sensor}}\left( {\chi,\beta^{\chi},\Theta} \right)} + {E_{shape}\left( {\chi,\beta^{\chi}} \right)} + {\sum\limits_{p = 1}^{P}{E_{pose}\left( \theta_{p} \right)}} + {\sum\limits_{p = 1}^{P}{E_{interpenetration}\left( {\chi,\beta^{\chi},\theta_{p}} \right)}}}$

It should be also noted that the terms in the objective functions canall be weighed by different scaling constants to change the relativeimportance of each term. This objective function is updated at each ICPiteration and optimized using the strategy described in Section 6.

SECTION 8. SIMULTANEOUS CAMERA CALIBRATION AND SHAPE RECOVERY

This section considers the more general and less constrained scenarioinvolving a moving person and one or more cameras where the camera(s)are not calibrated. Camera calibration is important for the accuraterecovery of body shape, as it specifies the geometric relationshipbetween the 3D world and the image plane (see section 2b). Previousmethods for body shape estimation have relied on using stationarycameras in a controlled environment, which allowed them to perform aseparate calibration procedure of the intrinsic and extrinsic cameraparameters independent of the images used for body shape recovery (Leeet al. 2000, Seo et al. 2006, Balan et al. 2007a). Here we focus on asingle uncalibrated camera case taking several images from multiplelocations, orientations and/or zoom. The case of multiple fixed camerasis formulated the same way but is simpler because image data can becaptured simultaneously so that the body may be treated as though itwere rigid. In the general case, a single camera is considered thattakes a sequence of images of a person in the scene. The scene isassumed to be rigid with the exception of the person who may change posebetween captured images and the camera may be moving as well. The personmay be wearing clothing or may be minimally clothed. While solutions tothe problem of estimating rigid scene structure from multipleuncalibrated images have been proposed in the literature, the moredifficult problem of estimating dynamic structure in the scene (i.e. theshape of a moving person changing their pose) from uncalibrated imagesis presently addressed. Also related is the work of Hasler et al.(2009a) who use multiple, unsynchronized, moving, butintrinsically-calibrated cameras for capturing human motion. They do notestimate body shape or use body shape in calibration but rather usestandard rigid-structure from motion methods applied to the rigidbackground scene.

The assumption of a calibrated camera is reasonable in many situationsof practical interest. Even with uncalibrated surveillance video,calibration can often be obtained using standard techniques (e.g. asdescribed in Hartley and Zisserman 2000). In general, for snapshots(e.g. from a cell-phone camera), calibration may not be available andany calibration information (even if only approximate) needs to beestimated directly from the images used to capture the subject, withoutrequiring a dedicated calibration procedure. Note that accelerometers orinertial sensors (e.g. as in the Apple iPhone) can provide informationabout camera motion that can help in this procedure. While there isliterature on both camera calibration and shape recovery (of visualhulls) from silhouettes (e.g. Boyer 2006; Criminisi et al. 2000;Hernandez et al. 2007; Yamazaki et al. 2007), the prior art does notaddress articulation or humans per se. These methods typically assume adense set of views of a rigid scene or strong restrictions on the typeof camera motion; none deal with non-rigid human pose variation.

Let Ψ={ψ₁, . . . , ψ_(P)} be the camera calibration parameters for Pimages taken by the same uncalibrated camera in different locations, oreven by different cameras. Each ψ_(p) contains the intrinsic andextrinsic parameters of the camera for each image (see Section 2b for adescription of the camera parameters). Note that all these parameterscan be estimated or the estimation can be restricted to a subset.Sometimes it is assumed that the focal length is known from EXIF dataand does not change; this assumption is not critical and can be relaxedto estimate focal length as well. Often one can also assume that theradial distortion is minimal for high-quality cameras.

The ψ_(p) parameters define the projection of the 3D body into the imagep. In the case of image silhouettes, the dependence on these parametersis made explicit in the prediction of the image silhouette. Thepredicted model silhouette for image p is written as

S_(p) ^(e)(χ,β^(χ),θ_(p),ψ_(p)).

Note that there is a different set of pose parameters θ_(p) for eachimage because the pose of the body may change, while there is a singleset of shape parameters β^(χ). The previous objective functions arerefined to allow optimization over the camera parameters

${{E_{Body}\left( {\chi,\beta^{\chi},\Theta,\Psi} \right)} = {\sum\limits_{p = 1}^{P}{D\left( {{S_{p}^{e}\left( {\chi,\beta^{\chi},\theta_{p},\psi_{p}} \right)},S_{p}^{o}} \right)}}},$

where D is the combined bi-directional silhouette error in the case ofno clothing (i.e. E_(1Pose;NoClothes;1Cam) ^(k) in Section 5a), or themore sophisticated error in the case of clothing (i.e.E_(1Pose,clothes;2D;1Cam) in Section 7a). In the case of moving cameras,the foreground regions S_(p) ^(o) can be found interactively or by usingstatistical segmentation methods (see Sections 2a and 2d). In oneembodiment, the GrabCut segmentation algorithm (Rother et al. 2004) isapplied after manually drawing bounding boxes around the subject in eachframe with a graphical interface.

Optimizing this function over the body shape β^(χ), multiple poses Θ andcamera parameters Ψ is often not sufficient as there are many unknownsand silhouettes provide limited constraints on the camera parameters.

To make the problem better constrained, several other optional terms areadded to the objective function. First, the segmentation of foregroundand background regions is exploited. This segmentation may be in theform of a binary segmentation or a tri-map that contains certainforeground, certain background, and uncertain regions (Section 2d). Theforeground is not rigid and the error term above accounts for this byallowing the pose parameters to vary. The background however can beassumed to be rigid. Estimating camera parameters for multiple views ofa rigid scene is a well understood Structure-from-Motion problem(Hartley and Zisserman 2000, Snavely et al. 2008). The novelty here isto ignore the known foreground, which contains the person, and only usethe background. Additionally, accelerometer or inertial sensormeasurements can be incorporated to constrain or replace the cameramotion estimation problem.

Hasler et al. (2009a) take an approach in which a person is moving in arigid scene. They use standard feature tracking and a robust RANSACmethod to ignore non-rigid parts of the scene that hopefully correspondto the moving foreground person. This gives the camera motion of therigid background; tracked points on the foreground person are treated asnoise.

In the present system a feature-based approach is employed:

-   -   1) Detect feature points f_(p,i) in the background regions of        each image p; e.g. SIFT features (Lowe 2004)    -   2) Establish correspondences between feature points in different        images (matching); using i to index corresponding feature points        and 1_(f) _(p,i) to denote if feature i was detected in image p    -   3) Given pairs of images with matching points, robustly estimate        initial camera parameters and the 3D location of the feature        points X=(X₁, . . . , X_(F)) while rejecting outlying matches by        minimizing the standard Structure-from-Motion objective function

${{E_{Rigid}\left( {\Psi,X} \right)} = {\sum\limits_{p = 1}^{P}{\sum\limits_{i = 1}^{F}{1_{f_{p,i}} \cdot {\delta \left( {\psi_{p},f_{p,i},X_{i}} \right)}}}}},$

-   -    where δ computes a robustified Euclidean distance between the        f_(p,i) image feature, if detected, and the projection its 3D        location X_(i) onto the image plane using camera parameters        ψ_(P).    -   4) Refine camera parameters through a global bundle-adjustment        phase (Hartley and Zisserman 2000), optionally incorporating        accelerometer or inertial sensor measurements of the camera        motion

In the present case the camera movement is expected to be small. It isalso expected that the person will fill a significant portion of theimage meaning that there will be relatively few background features tomatch. The person may also be photographed against a fairly plainbackground, further reducing feature matches. Finally, there may not bevery much depth variation in the background. Consequently the standardestimation of camera parameters alone may not be very accurate.

To deal with this, the objective function for the body pose is combinedwith the rigid background term

E _(Calib1)(χ,β^(χ) ,Θ,Ψ,X)=E _(Body)(χ,β^(χ),Θ,Ψ)+E _(Rigid)(Ψ,X).

Note that the camera parameters for a given image have to be the samefor both the foreground (non-rigid body) and background (rigid) scene.

Note that the rigid term uses features in the scene. Its performance canbe improved by adding special features to the environment. For example,the user can print out a checkerboard grid of known dimensions on apiece of paper and put it at their feet. In this case, the each cameraview can be solved for easily as the problem reduces to a standardcamera calibration problem. If the grid is small however, additionalconstraints may still be needed.

Additionally, there is no need to solve a general camera calibrationproblem. The photography of a person is a much more constrained problem.People tend to take photographs by either holding a camera viewfinder upto their eye or by viewing the display of a digital camera slightlylower than eye level. The camera orientation is also constrained by theheight of the camera, the field of view and the height of the subject.Consequently, a “prior” is formulated on the camera calibrationparameters that is specific to this problem. Previous, more general,priors have been used for calibration (Fitzgibbon et al. 2007); thatwork assumed the prior was unknown but shared among a set of stereocameras. Here we assume a known prior, which can be learned fromexamples of people taking pictures of other people in an environmentwith calibration objects present. Alternatively the priors can be set“by hand”. For example, if we know the camera is held upright (no tilt),this can be “built in” as a “hard” prior on camera orientation. In thesecases the new objective becomes

E _(calib2)(χ,β^(χ) ,Θ,Ψ,X)=E _(body)(χ,β^(χ),Θ,Ψ)+E _(Rigid)(Ψ,X)+E_(CamPrior)(Ψ).

In one embodiment E_(CamPrior)(Ψ) is a Gaussian probability distributionaround the mean value for each parameter (or the von Mises probabilitydistribution for the rotation parameters), however it can be extended toa mixture of Gaussians to deal with the multi-modal distribution oncamera height. Not all camera parameters must be estimated in allapplications. In some situations it may be sufficient to estimate cameraorientation relative to the person or the ground plane (Hoiem et al.2006, 2008). Hoiem et al. (2006) note that a reasonable prior on cameraheight places it at approximately 1.67 m above the ground, correspondingto the average eye level of an adult male.

Finally there is one other valid assumption in the present case that canimprove accuracy. It can be assumed that the camera orientation (andposition) is similar between every snapshot. This provides a “temporalprior” on the camera parameters that penalizes large changes inorientation for example. Again this prior can be learned from trainingexamples of people taking several photos of another person or can be setby hand. If the number of camera views is small the prior can be appliedto every pair of views or, in general, the prior is only applied toneighboring views in a sequence as follows

${E_{{Calib}\; 3}\left( {\chi,\beta^{\chi},\Theta,\Psi,X} \right)} = {{E_{Body}\left( {\chi,\beta^{\chi},\Theta,\Psi} \right)} + {E_{Rigid}\left( {\Psi,X} \right)} + {E_{CamPrior}(\Psi)} + {\sum\limits_{p = 2}^{P}{\rho_{1}\left( {\psi_{p - 1},\psi_{p}} \right)}}}$

where ρ₁ is a penalty function defining the Euclidean distance betweencamera parameters and the images are temporally ordered from 1 to P.

Note that this formulation provides a method for extracting camera poseand body shape over an image sequence such as television sequence. Inthat case a prior can also be placed on the temporal change in body poseto enforce that the pose changes slowly from frame to frame

${E_{Sequence}\left( {\chi,\beta^{\chi},\Theta,\Psi,X} \right)} = {{E_{Body}\left( {\chi,\beta^{\chi},\Theta,\Psi} \right)} + {E_{Rigid}\left( {\Psi,X} \right)} + {E_{CamPrior}(\Psi)} + {\sum\limits_{p = 2}^{P}{\rho_{1}\left( {\psi_{p - 1},\psi_{p}} \right)}} + {\sum\limits_{p = 2}^{P}{\rho_{2}\left( {\theta_{p - 1},\theta_{p}} \right)}}}$

where ρ₂ is a penalty function defining the Euclidean distance betweenpose parameters. Analogously, body shape could be allowed to changeslowly as a function of time by enforcing a prior favoring small changesin β^(χ). Finally, as with any of the objective functions defined above,they can be augmented to include the pose and shape priors described inSection 6b. The terms in the objective functions can all be weighed bydifferent scaling constants to change the relative importance of eachterm.

The optimization can be done using a gradient-free direct search simplexmethod as described in section 6a. To avoid getting stuck in localoptima, the following strategy may be used in optimizing the objectivefunction:

-   -   1. Segment the images into foreground and background regions. In        the clothes case, also identify skin and clothed regions.    -   2. Perform standard robust Structure-from-Motion on the putative        background region of the images to obtain initial estimates for        Ψ and X. Here, alternate between optimizing calibration and 3D        feature locations using E_(Rigid).    -   3. Alternate between optimizing body model parameters and camera        calibration parameters using E_(Sequence), or E_(Calib3), and 3D        feature locations using E_(Rigid).

SECTION 9. MATCHING

A body-shape matching component searches a database of body shapes tofind shapes that are similar to a user's shape. This component uses amatching function to determine how similar two different body shapesare. There are many methods for matching 2D or 3D shapes. A commonmethod for comparing 3D shapes uses spherical harmonics (Funkhouser etal. 2005). These methods are particularly appropriate when the shapesare very different. When the shapes are similar like human bodies, andthe meshes are aligned as in the present case, much more precisemeasures can be used.

Many efficient database search methods for this kind of problem are wellknown in the art and include methods like KD-trees, nearest neighborsearch and locality sensitive hashing (Andoni and Indyk 2008). For smalldatabases, even exhaustive search works well. The choice of searchalgorithm is not considered further, rather focus below is on the choiceof distance measure.

Four classes of matching will be considered here, as follows:

-   -   1. Body shape matching incorporates the global overall shape        similarity between bodies.    -   2. Measurement matching incorporates the comparison of        traditional 1-dimensional measurements that are possible to make        by hand, but which can also be inferred from a 3D body shape        model.    -   3. Ancillary matching incorporates information that does not        directly determine (but may be correlated with) shape. Ancillary        data may include information about clothing or other products a        person has purchased or rated.    -   4. Product matching incorporates information about a specific        product of interest to the match. This may include user-supplied        ratings of the product such as a “fit” rating.        These matching terms are combined to produce a match score.

Previous methods for sizing clothing from measurements have relied onmatching tailoring measurements or categorical information (such as“hourglass” or “pear shaped”) supplied by users (Rose 1999; Wannier andLambert 2006) or derived from 3D body scans (Wang 2005). None of thesemethods directly match 3D body shape representations. As subsequentlydescribed, 3D body shape matching is combined with these other methodsas an option.

Matching Body Shapes

Euclidean vertex distance. Given aligned body models, it is possible tosimply compute the (square) distance between then as the average(square) distance between all the vertices, v_(1,i) and v_(2,i) in twomodels

$d_{Verts}^{2} = {\frac{1}{N}{\sum\limits_{i = 1}^{N}{{v_{1.i} - v_{2,i}}}^{2}}}$

where N is the number of vertices in the model. This distance takesadvantage of the fact that the model factors pose and shape, allowingboth models to be placed in the same pose before comparing them, but itdoes not explicitly model “shape” and is disproportionately affected byheight. This can be mitigated by first height normalizing the verticesto a common height; depending on the application, this distance may bepreferred normalized or un-normalized. The squared distance may also bereplaced by a robust function to produce a robust distance measure.

Shape coefficient distance. Given the learned shape deformation modelsfor a population, the shape of a person is approximated as a linearcombination of basis shapes. The linear coefficients, β, can be used tomeasure distance

$d_{Body}^{2} = {\frac{1}{K}{\sum\limits_{j = 1}^{K}{\left( {\beta_{1,j} - \beta_{2,j}} \right)^{2}/\sigma_{i}^{2}}}}$

where K is the number of bases used in matching, σ_(i) ² is the variancealong each principal component direction (as defined by the eigenvaluescomputed during PCA). The use of the normalizing terms, σ_(i) ², isoptional and they may all be set to 1. Using the estimated σ_(i) ² givesthe Mahalanobis distance, which has the effect of increasing theimportance of the shape variations that account for less of the actualvariation between people. Often the principal components accounting forthe largest variation are more related to perceived differences inshape. Consequently, better shape matching is achieved by setting thescaling values to 1. It should be understood that the squared distancecan be replaced by a robust distance function, which may also depend onσ_(i) ².

Shape coefficients provide a good foundation for comparing two bodyshapes. By definition they capture important shape variations across thepopulation. Some shape variations may not be important in someapplications however. The face region is one example. The importance ofthe face (or other region) can be decreased or eliminated by usingweighted PCA. This is described in Section 10 on prediction fromspecialized shape coefficients.

Shape transformations. While shape bases are useful for matching, othershape features can be used. For example, spin images (Johnson 1997) canbe used to define a shape descriptor and used to match bodies. Anguelovet al. (2005) used PCA-compressed spin images to align meshes. In thepresent invention, spin-images are used in a different way to defineshape descriptors that can capture the shape of the body, eitherglobally or locally, and then used to match a given body into a databaseof bodies that are already in correspondence.

An alternative is to define a radial distance feature in 3D. This isanalogous to the 2D radial distance function used in Section 4(Initialization) and is made practical by the alignment of the bodyshapes. The centroid of the body is computed from the vertices and thedistance to a pre-defined subset of vertices is computed. This gives afeature vector that may be used as is, or compressed (e.g. with PCA orvector quantization). Matching into the database then uses distancesbetween the feature vectors, which can be trivially computed.

Matching Measurements

The matching of user measurements to a database has been described inSection 4d. For initialization, these measurements are provided by theuser. For matching, however, they may also be generated from the bodymodel using any of the measurement methods described in Section 10(Extracting Measurements).

$d_{Measure}^{2} = {\sum\limits_{i = 1}^{m}{\left( {{f_{i}\left( \beta_{1} \right)} - {f_{i}\left( \beta_{2} \right)}} \right)^{2}/\sigma_{i}^{2}}}$

where m measurements, f_(i)(β₁), are made from the body and where thevariance associated with each measurement is σ_(t) ².

Matching Ancillary Data

In addition to body shape, matching two people can take into accountother features such as age, ethnicity, clothing size preference andother ancillary data. The database of stored body shapes may haveancillary data such as clothing brands and sizes that fit well. Forexample, when a person orders clothes using their body model through anon-line retailer, they can provide feedback about the clothing and howit fits using a rating system and text input. This information is storedin the database along with their body shape model.

In addition to linear and circumference measurements, non-metric ordiscrete properties such as clothing sizes or body types may be used inthe match. For discrete measures that are represented by non-numericvalues (e.g. bra cup size, build type, or “petite”), a distancefunction, d_(i)(value1, value2), is defined that returns a numeric valuefor ancillary data type i.

One method for doing this is to convert the discrete measures intonumeric values. For bra cup sizes for example, this is straightforward.Another example is shoulder slope which can be discretized into a fewcategories like “square”, “sloped” or “very sloped”; these can be mappedto the values 1, 2, 3 for example. The distance is then computed usingthese numeric values with a possible scaling constant to make thedistance commensurate with the linear and circumference measures.

Some categories like ethnicity are best represented by a scaled binaryvalue. People of the same ethnicity, for example, would have a distanceof 0 while any difference in ethnicity would give a positive constantdistance.

More generally, a lookup table is defined that specifies the distancebetween A ancillary values. These too may be individually scaled withweights determining the importance of each term

$d_{Ancillary} = {\frac{1}{\sum w_{i}}{\sum\limits_{i = 1}^{A}{w_{i}{d_{i}\left( {a_{1,i},a_{2,i}} \right)}}}}$

where a_(j,i) is the ancillary value i for body j and each d_(i) is afunction (e.g. lookup table) that returns the distance between thevalues of type i.

Product Matching

In addition to body shape, the match score may take into accountinformation about products such as clothing. A distance d_(2 prod) (p₁,p₂) is defined between products. This may be implemented as a lookuptable. Let p_(i) be a vector of clothing descriptors such as [Brand,Gender, Clothing_Type, Style, Size]; for example [Gap, Women, Jeans,Relaxed, 8]. The product distance function returns the distance betweenany two such descriptor vectors. If a value is missing it can berepresented by NA. An exact match of brand, clothing type, style andsize could be assigned a distance of zero. A match that only includesbrand, clothing type and size can be assigned a higher value.Differences in size produce proportionally higher distances.

In a typical scenario, a person with body β₁ (called the probe) wishesto know if a particular garment with properties p₁ will fit them.Consider a potentially similar body, β₂, (called the test) that may havemany product vectors associated with it.) Let p_(j)(β₂ ^(ID)) be thej^(th) such product vector of this test body where β_(i) ^(ID) is usedto denote the unique database identifier for body i. The productdistance between probe and test bodies is defined as

${d_{Product}\left( {p_{1},\beta_{2}^{ID}} \right)} = {\min\limits_{j}\left( {d_{2{prod}}\left( {p_{1},{p_{j}\left( \beta_{2}^{ID} \right)}} \right)} \right)}$

where the closest matching (minimum distance) product vector is foundand this distance is returned as the overall match.

More generally, if the product of interest is not known, then a generalproduct distance between two bodies can be computed as

${d_{{Product}\; 2}\left( {\beta_{1}^{ID},\beta_{2}^{ID}} \right)} = {\min\limits_{i,j}\left( {d_{2{prod}}\left( {{p_{i}\left( \beta_{1}^{ID} \right)},{p_{j}\left( \beta_{2}^{ID} \right)}} \right)} \right)}$

which finds the two most similar product vectors for the two bodies andreturns their distance.

Additionally, stored in the database with information about products isoptional user-supplied ratings. The ratings can be used to augment theproduct match score; for example by adding a constant to it. A highrating could add zero while a low rating could add a large constant. Inthis way, both similarity of the item and its rating are combined.

Combined Distance

Combinations of these different matching distances may be used inweighted combination. For example

Match(β₁,β₂)=w ₁ d _(Body)(β₁,β₂)+w ₂ d _(Measure)(β₁,β₂)+w ₃ d_(Ancilary)(β₁ ^(ID),β₂ ^(ID))

where the w_(i) are weights that can be varied relative importance ofthe terms and If product-based matching is desired, this becomes

Match(β₁,β₂ ,p)=w ₁ d _(Body)(β₁,β₂)+w ₂ d _(Measure)(β₁,β₂)+w ₃ d_(Ancilary)(β₁ ^(ID),β₂ ^(ID))+w ₄ d _(Product)(p,β ₂ ^(ID))

Note that setting w₁, w₂, and w₃, to zero produces a match score thatdepends only on product information and ratings.

SECTION 10. EXTRACTING BODY MEASUREMENTS

Most of the methods for body shape estimation have had the goal of usingthe body shape to extract various measurements. These could be linearmeasurements such as height, circumferences such as waist size, volumes,or weights. Measurement extraction has many applications in fitness andweight loss, health care, clothing pattern making, and clothing sizingto name a few. Other types of information can also be extracted frombody shape models, many of which have not previously been addressed suchas gender, ethnicity, age, posture, body mass index (BMI), fitnesslevel, etc.

Most previous approaches work directly on the geometry of an individualbody scan. Typical scanners return a “cloud” of points, which is thentriangulated to produce a 3D mesh model. Each scan produces a differentmesh and scans of different people produce very different meshes. It istypically assumed that the body is in a known canonical (standard) pose.In this case, where the meshes are not in correspondence, the standardmethod for extracting measurements involves computing distances on thesurface of the mesh. There are several ways this is done. For linearmeasurements between two points on the surface one can compute theEuclidean or geodesic distance. The geodesic distance can be constrainedto lie along a path passing through certain landmarks. Computingcircumferences involves “slicing” the mesh with a plane by computing theintersection of the triangles of the mesh with the plane. Theintersection gives a closed contour and the length of this contour givesthe circumference. Sometimes it is preferable to compute the convex hullof the contour as it may correspond better to the measurements obtainedby a standard tape measure on the real body. Slices can be taken throughthe body shape model at any orientation. For example, given theorientation of the upper arm, a slice perpendicular to this orientationgives the perimeter of the arm at a given location. This can be appliedto any part of the body. A slice may intersect more than one body part(e.g. both legs). If so one must segment the slice into parts. This canbe problematic when body parts are touching (e.g. measuring the girth ofthe thigh when the inner thighs of a heavy person touch).

10a. First disclosed approach to body measurement extraction Posing formeasurements. We refer to the measurement method discussed above as the“standard” approach. Having a parametric body model that factors shapeand pose provides significant additional capabilities and benefits.Specifically, the pose of the body can be changed without changing theunderlying identity of the person. So, for example, if the person isscanned in a relaxed pose (arms at their side), their arm span can bemeasured by transforming the mesh into a “T” pose as described inSection 3 and then measuring the distance between the wrists. Acomplicated geodesic distance measurement is thus transformed into asimple Euclidean distance measurement.Measuring parts. Additionally, because the body model is segmented intoparts, by construction (Section 3), the body can be sliced on a planeand one can determine which intersections correspond to which parts. Forexample, the intersection can be performed with only the part ofinterest. In the case of the thighs as noted above, this allowsmeasurement of each thigh without an additional and difficultsegmentation of the plane intersection.Knowing where to measure. Finally, where one measures the body iscritical for accuracy. With standard body scans, feature points must beidentified and this can be difficult if there is noise in the scan. Forexample, arm length requires the identification of the shoulder and thewrist, both of which can be difficult to locate in standard scans. Givenbody models that are all in alignment as described herein, thesefeatures can be determined once on any individual mesh and the vertexlocations are then automatically known on all other meshes.

To locate landmarks with accuracy greater than the resolution of thepresently disclosed model, training scans are taken with known locationsof key points on the body. A function is then learned mapping verticesto the location of the key points. Typically a local neighborhood ofvertices (or global shape parameters) is taken and linear regression isused to learn this prediction function (details of the linear predictionmethod are presented in Section 10b).

This same method can be used to learn where to slice the body and atwhat angle. For example, determining the correct height and angle formeasuring the waist is a known and difficult problem. Given trainingexamples of the correct parameters of the intersecting plane, a mappingis learned from vertices of the body (or global shape parameters) toplane parameters.

Measuring the waist for pants is known to be particularly difficultbecause personal preference (related to body shape) varies where thismeasurement should be taken. A machine learning approach (Section 10d,below) is used to match a body to a database of bodies with ancillarydata specifying body measurements as well as where to measure the body.Combining information from the best matching bodies gives a predictionfor where to measure a new body.

This statistical learning approach for determining where and how to takestandard measurements is one example of a more general and powerfulstatistical approach described in detail below.

10b. Second Disclosed Approach to Body MeasurementExtraction—Statistical Approach

The statistical method for estimating body measurements discussed belowalso differs significantly from the standard approach noted above. Thisstatistical method uses the fact that all the body models are incorrespondence and that the shape of the body has been characterized bya small number of parameters. The general formulation involves usingtraining data containing body models and the desired measurements andlearning a function that maps shape information to measurements:

measurement=f(body shape).

The measurement can be any of the standard measurements described abovesuch as locations of landmarks or parameters for standard measurementtechniques. The measurement may also be other personal data thatcorrelates with body shape, such as age. The body shape information canbe any shape descriptor computed from the body model. In one embodiment,the body shape information is taken to be the linear coefficients, β,characterizing the shape of the body. Linear or non-lineartransformations of the mesh, filtering, spin images, spectralcomponents, the mesh Laplacian, etc. could all be used as input. In thisembodiment the function f(.) is taken to be linear, but it could benon-linear, a mixture of experts, non-parametric, etc. In particular,f(.) could be implemented non-parametrically using nearest-neighborsearch (Section 10d). In the non-parametric form, the matching functiondescribed in Section 9 is used to find the N closest bodies and thentheir stored measurements are combined to produce a weighted combination(e.g. weighted mean or median). The linear version is presented indetail but it should be clear to someone practiced in the art that otherstandard functions could be used.

Allen et al. (2003, 2004) considered the related problem of predictingbody shape from measurements (Section 4). Like the first method belowthey used a linear prediction function. They did not consider the caseof predicting measurements from shape coefficients. The presentdisclosure goes further to predict measurements from properties of thebody such as vertices or functions of vertices and shows how to selectthese properties or vertices automatically.

Prediction from Shape Coefficients

First considered is the case of predicting measurements from shapecoefficients, β. Given a training database containing n body shapes withknown measurements, the following system of linear equations is defined

$m_{i} = {\begin{bmatrix}m_{i,1} & m_{i,2} & \ldots & m_{i,n}\end{bmatrix} = {{f_{i}\begin{bmatrix}\beta_{1,1} & \beta_{1,2} & \ldots & \beta_{1,n} \\\beta_{2,1} & \beta_{2,2} & \ldots & \beta_{2,n} \\\vdots & \vdots & \; & \vdots \\\beta_{k,1} & \beta_{k,2} & \ldots & \beta_{k,n} \\1 & 1 & \ldots & 1\end{bmatrix}} = {f_{i}B}}}$

where m_(i,j) is measurement i for body j and β_(q,j) is the linearcoefficient q for body j. Here it is assumed the bodies are representedby k linear basis shapes. The linear “filter”, f_(i), maps shapecoefficients to single measurements and can be learned using leastsquares estimation

f _(i) =m _(i) B ^(†) =m _(i)(B ^(T) B)⁻¹ B ^(T),

where B^(†) is the pseudo-inverse of B.

Typically hand measurements are used to obtain the ground truth data inm_(i). These are often inaccurate, and consequently one can use robustregression rather than least squares, such as a standard iterativelyre-weighted least squares method with a robust penalty function. Theexact choice of penalty is not critical.

Given a new body that is not in the training set, the measurement m_(ij)is predicted from the coefficients β_(j)=[β_(1,j), β_(2,j), . . . ,β_(k,j),1]^(T) as m_(ij)=f_(i)β_(j). Note, more generally, the trainingvector m_(i) can be replaced by a matrix M containing severalmeasurements for each training subject and then f_(i) becomes a matrix Fthat maps body shape parameters to many measurements simultaneously:M=FB.

Prediction from Specialized Shape Coefficients

The shape coefficients, β, are global descriptors of shape—varying oneshape coefficient may vary the shape across the entire body.Measurements however are typically quite local. Details of facial shapefor example may be only weakly correlated with the shape of the waist.Consequently more local measures of body shape are optionally used.Specifically, different shape subspaces are computed that focus on theproperties of interest. For example, one can compute a new shapesubspace that ignores the vertices of the face. Prediction ofmeasurements from shape coefficients in the restricted space ignores anyvariation due to face shape.

Correspondence of all vertices across all models allows such subspacesto be found by weighted PCA where a low weight (e.g. zero) is given tocertain vertices or triangle deformations. This can also be done at apart level. For example, a shape subspace can be constructed for justthe torso region and the coefficients of this model used to predictmeasurements related to the torso such as chest circumference.

Given a body shape defined with the standard deformation subspacecoefficients, β, this needs to be related to the reduced subspacemodels. The β coefficients define a deformation of every triangle in themodel. This deformation is taken and projected onto the new specializedsubspace. If some weights were zero during PCA learning the resultingsubspace will be orthogonal to them and they will not have any affect inthis projection. The resulting projection gives a new set of linearcoefficients, β′, in the specialized subspace. These coefficients arenot generic in that they cannot synthesize any body shape but rathercharacterize the amount of deformation of particular sub-areas of thebody.

Additionally, the standard shape basis is designed to allow thegeneration of arbitrary human body shapes. Generative models such asthis are not always the best for detailed analysis. To address this,other transformations of the mesh can be used that accentuate relevantshape aspects of the body. One embodiment computes a spin-imagerepresentation (Johnson 1997) of each body and then computes alow-dimensional model of these representations. Measurement predictionis then made from these coefficients in the same way as described abovefor the standard shape basis. Below, when discussing prediction fromvertices, it should be understood that the 3D location of the verticesof the model can be replaced by some other representation such as aspin-image, mesh Laplacian, or local curvature representations.

Prediction from Vertex Coordinates or Derived Predictors

Another way to focus on local shape properties relevant to a specificmeasurement is to replace the matrix B above by a matrix of 3D vertexcoordinates instead. To focus on specific parts of the body, a subset ofthe vertex coordinates {x₁, y₁, z₁, . . . , x_(n) _(V) , y_(n) _(V) ,z_(n) _(V) } that are most relevant for predicting a specificmeasurement is selected. There are several methods that can be used toselect the subset.

Using a Random Subset of Vertices.

A simple method that works surprisingly well is to select a randomsubset of vertex coordinates to form the rows of a matrix B, whosecolumns span all the training examples. This method effectively spreadsthe selected vertices uniformly over the whole body. If a given vertexcoordinate has low predictive value, regression will automatically giveit a low weight in the filter f while more predictive vertex coordinateswill be given higher weights.

Greedy Selection of Correlated Vertices.

Another way to select a subset of vertex coordinates is to choose thosethat are highly correlated with the measurement of interest (thiscorrelation can be computed for every vertex coordinate). Often many ofthe vertex coordinates will be highly correlated with each other andtherefore are redundant. To select a small, yet predictive, group a“greedy” approach is employed.

Given a subset of i−1 vertex coordinates selected from {x₁, y₁, z₁, . .. , x_(n) _(V) , y_(n) _(V) , z_(n) _(V) }, in accordance with thedisclosed method, an i^(th) vertex coordinate is chosen to add to thesubset. This is accomplished by first robustly estimating the bestlinear filter, f, that predicts the desired measurement vector from thei−1 vertex coordinates. The prediction is then subtracted from the knownvector of the true measurements, m, for all the bodies. This defines aresidual vector, m*. To select the i^(th) vertex coordinate, thecorrelation, r_(j)(m*), of each vertex coordinate, v_(j), with theresidual vector is computed. The vertex coordinate that maximizes thiscorrelation is taken and the process repeated.

In pseudo code, the method is

V₁ := { argmax_(j)(r_(j)(m)) } for i from 2 to k do f_(i−1) :=robustfit(B(V_(i−1)), m) m* := m − f_(i−1) B(V_(i−1)) V_(i) := {V_(i−1), argmax_(j)(r_(j)(m*)) } end forwhere V_(i)={v₁, . . . , v_(i)} is the currently selected set of ivertex coordinates, m* is the residual error between the ground truthvector of measurements, m, and the current prediction. B(V_(i)) is thematrix of vertex coordinates whose rows are the subset of vertexcoordinates V_(i), and whose columns span all the training examples. Themethod robustfit(B(V_(i−1)), m) is a robust version of the standardleast-squares problem: f_(i−1)=mB(V_(i−1))^(†).

Note that rather than use vertex coordinates, the output of any filterapplied to the vertices could be used instead and the same methodsdescribed will work. For example a filter that computes local surfacecurvature (e.g. second derivative of the surface) could be used insteadof vertex coordinates.

Predicating Multiple Measurements.

The greedy method above is defined to predict a single measurement foreach body and finds a set of vertex coordinates or other parameters thatlinearly predict that measurement. It is often useful to predict severalmeasurements from the same subset of vertex coordinates. Consequently asingle set of vertex coordinates or other parameters is sought thatsimultaneously predict a set of body measurements.

The algorithm is modified from above

V₁ := { argmax_(j)(c_(j)(M)) } for i for 2 to k do F_(i−1) :=robustfit(B(V_(i−1)), M) M* := M − F_(i−1) B(V_(i−1)) V_(i) := {V_(i−1), argmax_(j)(c_(j)(M*)) } end forwhere the vector of measurements has been replaced by a matrix M, thefilter by a matrix F, and the residual function by a cost function,c_(j), that combines information from many measurements.

Let r_(j)(M_(k)) be the correlation of vertex coordinate j to themeasurement (or residual) M_(k) where k selects the row of Mcorresponding to a particular measurement (or residual) across all thebodies. Now, rather than selecting the vertex coordinate that maximizesr_(j) for a single measurement, multi-measurement method computes thevertex coordinate that is “best” in some sense for all the measurements.This means combining information from the predictions for multiplemeasurements into a single value denoted c_(j)(M*). There are many waysto do this. The simplest but most computationally expensive way is tosimply fit (robustly) a new prediction matrix F for the addition of eachpossible vertex coordinate, use that F to predict all the measurementsand choose the vertex coordinate that produces the lowest residualerror. With a large number of vertex coordinates this becomesimpractical so an approximate method is employed in one embodiment.

The goal is to choose a vertex coordinate that is “good” in the sensethat it reduces the residual errors in predicting all the measurements.Intuitively it may be desirable to favor the accurate prediction of somemeasurements over others. For example, it may be desirable to favor theprediction of measurements that have high variance in the training set.Let be the variance of measurement k across the training set of bodies.Then the cost function is defined as

${c_{j}\left( M^{*} \right)} = {\sum\limits_{k = 1}^{n}{\sigma_{k}^{2}{{r_{j}\left( M_{k}^{*} \right)}.}}}$

where n here denotes the number of measurements. This combines thecorrelations for each measurement (appropriately weighted) into a singlescore for vertex coordinate j.

Predictions for Sub-Populations

In the above discussion all the bodies in the database have been treatedequivalently and a single mapping from bodies to measurements has beenlearned. Of course men and women have different shapes and the optimalmeasurement predictions may use different shape coefficients orvertices. The same is true for different ethnic groups or age groups.For example, one can learn a predictor for Asian women, athletic women,or men under 30 years of age. Consequently prediction functions aredefined for different sub-populations. Then, when estimating bodymeasurements, if the sub-population is known, the appropriately trainedmodel is used for prediction. If not, then a generic model is used. Themodel of the greatest specificity is used.

10c. Discrete Measurements

The discussion above has focused largely on continuous measurementswhere the mapping can be represented by linear or non-linear functions.There are many discrete, or categorical, measurements that are also ofinterest and that can be estimated from body shape. Examples includediscrete sizes such as dress size, jacket size, bra cup size, etc. Fornon-numeric measurements (e.g. cup size), if there is a natural order tothe sizing, it can be converted to a continuous scale by mapping it tothe real line. For example, women's bra cup sizes can be mapped from A,B, C, D, etc. to 1, 2, 3, 4.

For some applications, qualitative judgments may be important. Forexample, when fitting a man's shirt, it may be valuable to classifytheir body type. Example classifications include:

Shoulder category

-   -   1 Normal    -   2 Slopping Shoulder Long Neck    -   3 Square Shoulder Short Neck

Upper Body Type

-   -   1 Slim    -   2 Regular    -   3 Fit    -   4 Athletic    -   5 Hefty

Mid-Section Type

-   -   1 Flat Stomach    -   2 Slight Stomach    -   3 Medium Stomach    -   4 Large Stomach    -   5 Hefty

Values such as these can be predicted in many ways. One is to convertthem to numeric values and use linear prediction (above) or the methodbelow. Alternatively, given a database of labeled bodies, any number ofmulti-class classifiers can be trained or nearest-neighbor matchingemployed (Section 10d).

Given numeric measurements, the regression methods described in section10b are used in one embodiment to learn a function from coefficients orvertex coordinates (or filtered values thereof) to the numeric values.Given a new body, the numeric value is predicted and the closestmatching numeric value is then found (e.g. by rounding the predictedvalue to the nearest integer), taking this to be the answer. However,when dealing with clothing sizes it is important to note that they arenot consistent between brands, models, and even production dates.Consequently, such predictions are best made for specific garments givena training set of body shapes for which that make, style and size areknown.

Gender

One important “discrete” measurement is gender. Automatically detectinggender is convenient for users and allows the use of gender-specificmodels and methods for fitting and measurement. Two methods aredisclosed for classifying gender.

The first uses the linear body shape coefficients, β. If a single PCAshape model is constructed with both men and women then it has beenobserved that the coefficients of men and women in this space are verydistinct. Classification of gender can be achieved using a simple linearclassifier though more complex methods such as support vector machinescould be used (Cristianini et al. 2000). These methods are standardclassification methods in the literature.

An alternative method fits separate male and female body models tosensor data and then evaluates how well they explain the measurements(e.g. silhouettes or range data). The model that produces the lowesterror is selected as the best fitting gender:

${\underset{\chi \in {\{{{male},{female}}\}}}{argmin}\left( {\min\limits_{\beta_{\chi},\Theta}{E\left( {\chi,\beta_{\chi},\Theta} \right)}} \right)}.$

Most previous work on gender classification from images has focused onfaces (e.g. Moghaddam et al. 2002), but in many situations the face maybe too small for reliable classification. The other large body of workis on estimating gender from gait (e.g. Li et al. 2008). Surprisingly,this work typically takes silhouettes and extracts information aboutgait while throwing away the body shape information that can providedirect evidence about gender. The presently disclosed approach is thefirst method to infer a parametric 3D human body shape from images ofclothed or minimally clothed people and to use it for genderclassification.10d. Non-Parametric Prediction Based on Body Matching

The above parametric linear methods can be extended to non-linearfunctions. FIG. 9 is a flow chart depicting a method employed forshape-based collaborative filtering. In the shape-based collaborativefiltering method, a body shape is matched to a database to find similarshapes. The stored measurement and size data for the best matchingshapes are then combined to produce an estimated measurement or size forthe input body.

More specifically, and referring to FIG. 9, if the database of bodyshapes and measurements 901 is sufficiently large, non-parametricmethods can be used. This approach uses the body-shape matchingcomponent 902 described in Section 9 to determine how similar two bodyshapes are. Given sensor data 903, body shape is estimated 904, forexample using one of the scanner embodiments described in Section 11, toproduce an estimated shape 905. Given a probe body shape represented byshape coefficients 905 and optional ancillary data such as age, gender,ethnicity, clothing sizes, etc. obtained, for example from a database908, the N closest matching bodies 906 in the database 901 can be found.The match score for each body j can be transformed to a value w_(j)between 0 and 1.

If the task is to extract waist size, for example, as depicted at step907 then this is computed from the N matching bodies 906. Each body j inthe database has stored with it the ground truth measurement orattribute m_(j). Consequently the N measurements are combined in one ofseveral ways such as the weighted average

$m^{*} = \frac{\sum\limits_{j = 1}^{N}{w_{j}m_{j}}}{\sum\limits_{i = 1}^{N}w_{i}}$

where the weight is derived based on the match distance between theprobe body and each of the N example matches. Alternatively the median

$m^{*} = {\underset{i}{median}\left( m_{i} \right)}$

is computed. Note m* has a different meaning here than in the Section10b.

This shape-based selective recommendation is referred to as shape-basedcollaborative filtering because it combines information from multiplepeople to make a recommendation for a new individual. Unlike othercollaborative filtering methods that, for example, match people based onmovie preferences, here the matching is based on body shape and optionalancillary information.

This method works well for predicting discrete clothing sizes,particularly since sizing varies significantly from brand to brand andacross clothing categories. In this case, the matching function can takeinto account whether an individual body in the database has sizeinformation for a particular garment (or category of garment) using theproduct match distance function (Section 9). Only bodies where relevantsize information is present are then included in the match and used tocompute the desired measurement (e.g. dress size). If, for example,sizing is desired for a particular brand and style of clothing, thematch function can be modified to address this requirement. This isimplemented including clothing brand and style information in theancillary or product match terms (Section 9). Body models that haveancillary product data corresponding to the desired brand and style aregiven a low distance while any body missing that brand and style isgiven a higher distance. The standard shape-based similarity terms thenweight more highly bodies that have similar shapes and have ancillaryproduct data about particular brands.

SECTION 11. SCANNING SYSTEMS

The methods described here can be configured in several ways to producedifferent types of body scanners using the techniques described in thepreceding sections (2-8). Four such systems are described.

11a. Changing Room Scanner

Described here is one of many possible scanning systems which may bebuilt using the techniques described in the preceding sections (2-8).The system consists of several cameras mounted on the walls of a smallroom or booth, as for example, a changing room in a retail clothingstore. In this system the environment is instrumented to simplifysegmentation and to deal with calibration. This scenario is most similarto existing body scanners in that it works in a controlled environment,but the presently described system is robust to variations in theenvironment over time and hence is appropriate for less controlledsettings.

A simple implementation of such a scanner involves mounting the camerasand calibrating them off-line. Additionally the background is paintedgreen or blue to allow segmentation based on chroma-keying.Unfortunately for such an implementation, vibration and customeractivity may cause camera extrinsic parameters to vary over time,introducing error into the estimated body shapes. Similarly, thecustomer may bring objects into the scanning room with them and leavethem in the field of view of the cameras. This means that simplycomputing foreground segmentation based on chroma-keying or simplebackground subtraction will produce inaccurate segmentations and thusinaccurate body shapes.

A pipeline is presently described for a changing room scanner thataddresses these considerations by automatic adaptation to the currentbackground and camera configuration.

A multi-chromatic calibration pattern on the floor and walls is used. Asdescribed in Section 2c, this pattern aids calibration withoutdetracting from segmentation. The changing room does not need completecoverage of the pattern, and may vary in paint color outside of thepattern; but better accuracy may be achieved with large patterns fillingthe field of view of each camera. The calibration can be checked foraccuracy with each image acquisition and automatically re-calibrated ifit is out of alignment (Section 2c).

During a scan, as illustrated in FIG. 10, a user stands in a knownlocation in an expected pose and images are acquired 1001. A region inthe image where the body could possibly be located is determined (e.g.background subtraction) in every camera view as depicted at block 1002.Background statistics (e.g. color and texture histograms) are computedfor each view in regions where the subject is not expected to belocated, as depicted at block 1003. Pixels (or regions of pixels) ineach view are compared to the background statistics by a classifiercomponent 1004 and classified as possible foreground or backgroundpixels using a simple threshold, resulting in an initial foregroundsegmentation 1005.

From the initial segmentation from multiple images 1008 and a roughlyknown pose, the body shape is coarsely fit 1006 to get an estimate ofthe height and overall build as depicted at block 1007 and described inSection 6. This is done by optimizing only the first few body shapecoefficients and the 3D position of the body while keeping articulatedpose fixed (this can be done at lower image resolution). With an initialguess of the body location and size, the segmented foreground regionsare refined using the tri-map method described in Section 2d.

With calibration and this refined segmentation, the standard fittingprocess described in Section 6 is used. In this scenario there may be nouser input of measurements, so individual-specific constraints may beunavailable. The system described here requires the user to stand in aparticular pose, but such a scanner may instead allow a variety of poses(Section 8) and clothing (Section 7) and use an automatic initializationalgorithm, as described in Section 4.

11b. Portable Scanner

The changing room scanner described above assumes multiple cameras thatare relatively fixed and mounted in the environment. These assumptionsare now relaxed and a system is described having a single camera that isheld by the operator. Using this single camera, one or more photographsare taken; since these frames are not acquired simultaneously, variationin the pose of the subject may occur from frame to frame.

One embodiment uses one or more MultiChroma Key grids (described inSection 2c) to enable simultaneous segmentation and calibration. Asingle grid placed on the floor is sufficient to enable extrinsiccalibration. A second grid can be placed behind the subject to aid insegmentation and provide further constraints on calibration.

Images are captured with the subject in several specified poses such asthose in FIG. 11. The objective function is optimized to solve for posein every frame, therefore variations in pose between frames isacceptable. If clothing is worn, a wider range of poses is typicallybeneficial to capture extra constraints on the underlying body shape(see FIG. 8).

The multi-chromatic grid is detected (Section 2c) in the images andcamera parameters are computed (Section 2b). Knowing the grid locationenables the identification of the multi-chromatic regions and thetraining of a statistical model of the color variation in them. Thisallows the foreground segmentation process to account for variations inlighting conditions that affect the measured color of themulti-chromatic calibration surfaces (Section 2c).

Segmentation is performed as defined in Section 2c. If the approximatepose of the subject is known, a separate initialization step isunnecessary. Given the foreground regions found using multi-chromakeying and a known initialization for pose, the method solves for thebody pose and shape following the procedure described in Section 6. Aconsistent shape is optimized across all images and the pose is allowedto vary in each image. Optionally the pose prior (Section 6b) is used toprevent the estimated pose from deviating too far from theinitialization. Also, optionally, user input is allowed for constrainedoptimization (Section 6b).

11c. Scanning from Snapshots

Body shape capture is now considered in a natural, un-instrumentedenvironment. Given the ubiquity of digital cameras in the marketplace(from high quality digital SLRs to cell-phone cameras), body shapecapture from such devices has the potential to make body scanningextremely accessible. While this general problem is challenging, thecomponents described here are assembled into a complete system to takeseveral snapshots and recover a full body model. A diagram for thissystem is shown in FIG. 12.

Referring to FIG. 12, the user obtains pictures of himself as depictedat block 1201 at several orientations—for example frontal, side and ¾views (see FIG. 11) and/or in several poses (see FIG. 8). The user maywear minimal or tight-fitting clothing, or may wear looser clothing inwhich case the optimization method described in Section 7 is used. Thephotos may be taken with a hand-held camera. The approximate positionand rotation of the camera should remain fairly constant between images(though a tripod is not necessary).

Height or other measurements 1202 may be provided by the user. Thesemeasurements 1202 are integrated into the objective function duringoptimization, as described in Section 6. In this uncalibrated case, atleast one body measurement (e.g. height) is needed to constrain theoptimization.

A putative segmentation for each frame is obtained using one of thesegmentation methods described in Section 2 or using input 1203 from theuser. For manual segmentation, the images are presented to the user on adisplay device and the user can either drag a rectangle over the regioncontaining the body, or can click on a few points which are used toobtain a rough body model using the method described in Section 4 fromwhich a tri-map is extracted as described in Section 2d. In either casethis is used as input to guide an image based segmentation algorithm1204, for example, based on graph cuts. In the case that the user isclothed, the image is segmented into three regions: skin, clothing/hairregions, and background. If the user is wearing tight-fitting clothing,then the image may be segmented into only foreground and background. Foreach frame, this produces a foreground silhouette and an optionalclassification for each foreground pixel as skin or non-skin asillustrated by regions 1205 (Section 2e).

Camera calibration is not available in the case of snapshots. The focallength, however, is typically available from the image's EXIF metadata1206. Other intrinsic parameters may be initialized to reasonabledefault values (no distortion, center of projection at mid-image), whichapproximately hold for most cameras (Hartley and Zisserman, 2000). Thesevalues are optionally used to initialize a standardStructure-from-Motion (SFM) algorithm that is applied to the backgroundregions across frames as described in Section 8 and illustrated at block1207. This produces an initial calibration 1208.

If the user adopts a pre-defined pose, no special initialization stepneed be performed. The body is initialized in the known pose with shapeparameters predicted from the input measurements (e.g. height, gender,age) as described in Section 4.

The shape, pose and calibration optimization 1209 is performed asdescribed in Section 8 to minimize, for example, E_(sequence).Optionally, the optimization 1209 alternates with the backgroundstructure-from-motion (SFM) component 1210, which updates the locationof 3D feature point locations X given the current camera calibrationparameters Ψ (see Section 8). This process converges to produce a poseand calibration for each frame and a single body shape as depicted atblock 1211.

11d. Surveillance Scanning

Unlike other technologies, the presently disclosed system can estimatebody shape using regular cameras and works when people are changing poseand wearing clothes. This enables an automatic method for acquiring aperson's measurements from surveillance cameras. This body shapeinformation may be used for several purposes depending on the scenario.

In a retail shopping scenario, multiple cameras capture the body ofcustomers as they move around a retail store. The system can be focusedon a specific region and activated when a person is detected enteringthis region. Detection can be performed using simple image differencingor auxiliary sensors such as motion detectors or force plates. Robustestimates of the background can be updated over time enabling effectivesegmentation of foreground regions; such algorithms have been describedin the literature.

Given multiple calibrated cameras and segmentation, the person's bodyshape is fit to the image data. An initialization component predicts oneor more possible body poses based on foreground silhouettes or otherimage features (Section 4). The body pose and shape estimationcomponents optimize the fit to the foreground silhouettes in each cameraas described in Section 6. Depth sensors (e.g. stereo or time of flight)may or may not be used, but when used, they help with both segmentationand shape estimation.

The clothing sensitive image error function is employed as describedSection 7 to provide an estimate of body shape under the clothing. Theestimated body shape and an image of the person's face may betransmitted to an in-store terminal and may be accessed by the customeror store clerk. The body shape model may then be used in any of theapplications described Section 12.

An alternative use of in-store cameras is for forensic video analysis.Here the estimation of height, weight, and other biometric informationcan be extracted and provided to police or matched against storedmeasurements to identify individuals based on body shapecharacteristics.

11e. Scanning with Range Sensors

The above embodiments focus on the use of standard digital cameras forestimating body shape. Of course, there are many other types of sensorsthat could be employed such as time-of-flight, stereo or structuredlight sensors that return information about scene depth. If the personis wearing tight fitting clothing, then a parametric body model can befit to this data using an iterative closest point (ICP) method, asdescribed in Section 5b, to first match the model vertices withobservation data points given an initial pose and shape and thenoptimize both pose and shape based on the matched 3D points. With a newpose and shape, the closest points are found again and the process isrepeated (See Section 5 for details). If the subject is observed inmultiple poses, the formulation in Section 6c is used to integrate shapeconstraints over multiple poses.

In many common scenarios such has home entertainment scenarios, users ofsuch a device are typically clothed. Thus the recovery of body shapeunder clothing remains a key issue. The method described here fits thebody shape under clothing in range imagery (Section 7). The basicprinciples are the same as for standard imagery: the true body shapefalls inside the measurements (clothing increases size), body shape isconstant across pose, clothing provides constraints on shape that varywith pose, and some regions of the body are observed with either noclothing or tight fitting clothing.

In Section 7 a modification to the standard ICP cost function isdescribed that allows clothing to be taken into account. Many rangescanning devices simultaneously acquire visible imagery, which eitherprovides a texture map or per-vertex coloration for the range data. Thisallows the classification of sensor data points as either skin orclothing using the skin classifier described in Section 2e (or moregenerally to classify each as corresponding to one of G classes usinguser input or skin/hair/clothing classifiers described in the literature(Section 7b)).

Given this classification, the clothing-aware ICP method alternatesbetween optimizing pose and shape using the cost functionE_(clothes;3D)(χ,β^(χ),Θ) defined in Section 7 and updating the closestpoints.

12. APPLICATIONS

This disclosure has described the core body shape estimation methods andseveral scanner embodiments that they support. Additionally these coremethods, combined with shape matching and shape measurement, support arange of applications. Each of these relies on the estimation of bodyshape from measurements (either sensor data or measurements such asheight and waist size). Given a parametric body model, the measurementand matching components are used in various ways below. Many of theseuses rely on a database of body models and associated ancillary data.

Body Shape Database

When a body model is created, it may be stored in a secure database witha unique identifier associated with a user. Specifically, the shapecoefficients are stored along with the version of the shape basis used(including the date of creation and whether it was created for asub-population). This allows the body to be reconstructed, matched ormeasured independent of when it was scanned. If a pair of bodies arecreated with two different shape bases, it is straightforward (givenvertex correspondence) to convert one or both of them into a commonbasis for comparison or measurement (Section 10). Additionally,ancillary data that the user enters may be stored such as their age,ethnicity, clothing sizes, clothing preferences, etc.

A user may access their body model in one of several standard ways suchas by logging onto a website over a computer network using a uniqueidentifier and password. The body model information may also be storedon a physical device such as a phone, key fob, smart card, etc. Thisportable version allows the user to provide their information to aretailer for example using an appropriate transmission device (e.g. cardreader).

The body identifier may be provided by the user to retailers, on-linestores, or made available to friends and relatives with or withoutprivacy protection. In providing access to their body model, the usermay provide limited rights using standard digital property rightsmanagement methods. For example, they may provide access to a friend orfamily member who can then provide their information to a clothingretailer, but that person could be prohibited from viewing the bodymodel graphically. As another example, a user could provide access todisplay the body to video game software to enable the use of the modelas a video game avatar, but restrict the further transmission of themodel or its derived measurements.

When a person purchases clothing from a retailer (e.g. over theInternet) using their body model, the size and brand information may be(optionally) stored with their body model. This information may beentered manually by the user with a graphical interface or automaticallyby software that collects the retail purchase information. Optionallythe user can provide one or more ratings of the item related to its fitor other properties and these may be stored in the database inassociation with the clothing entry.

If a person has multiple body scans obtained on different dates, theymay all be maintained in the database. The most recent model can be usedby default for matching and measurement. When ancillary data is stored,it is associated with the most current scan at that time. Additionally,storing multiple body models enables several applications. For example,body measurements can be extracted and plotted as a function of time.The shape of the body can also be animated as a movie or displayed so asto show the changes in body shape over time. One method provides agraphical color coding of the body model to illustrate changes in bodyshape (e.g. due to weight loss). Since all model vertices are incorrespondence, it is easy to measure the Euclidean distance betweenvertices of different models. This distance can be assigned a color froma range of colors that signify the type of change (e.g. increase ordecrease in size as measured by vertex displacement along its surfacenormal). Color can alternatively be mapped to other shape attributes(such as curvature) computed from the mesh. The colors are then used totexture map the body model for display on a graphical device.

Shape-Based Collaborative Filtering

Collaborative filtering or recommendation uses information about manypeople to predict information about an individual who may shareattributes in common with others. A common example is movie ratings. Ifmany people who liked movie X also liked movie Y, an individual wholiked X but has not seen Y may reasonably be expected to like Y.

A new form of collaborative filtering based on 3D body shape ispresently disclosed. People with similarly shaped bodies may be expectedto be interested in similar products such as clothing or weight lossproducts. Specifically if many people with similar body shapes to X buypants of size Y, then an individual X may also be expected to fit sizeY. Thus, a body shape model is used as described to match people basedon body shape (Section 9 and 10d).

Several embodiments of this method of body shape matching are possible.

-   -   1. Size recommendation. If a user is shopping for clothing of a        particular type, the system identifies N people with similar        body shapes (Section 9 and 10d) for whom ancillary data related        to this (or similar) item is stored in the database (e.g. use        the product distance function). A function is used (e.g. a        weighed combination based on body shape distance) to predict the        best size (Section 10d). Body shape as well as similarity in        clothing preference may be used in the matching (Section 9).    -   2. Community ratings. Instead of being presented with a specific        size, the user is presented with a list of ratings for the        product by people of similar size. The degree of similarity is        shown along with optional entries such as the rating, comments,        photos, etc. The degree of similarity can be expressed on a        point scale or percentage scale by taking the body shape        distance measure (Section 9) and normalizing it to a new range        (e.g. 1-100 where 100 is an exact match and 1 is the match to a        very different body shape).    -   3. Community blogs. People with similar body shapes may be        trying to lose weight or increase their fitness. Shape-based        matching is used to find people with similar body shapes. Groups        of people with similar shapes (an possibly preferences) define a        “community”. Users can post information (e.g. in a blog format)        about themselves and find postings by other members of the        community who of similar shape (or who have undergone as similar        change in shape). The key concept is that community is defined        based on body shape-related properties.

Matching Using Fit Models

A method of performing matching using fit models is illustrated in FIG.13. A seller of a particular garment can associate a body shape, or fitmodel 1303 with a garment where that body is known to fit that garment.For example an individual wants to sell an item of clothing that fitsthem through an on-line auction. They list the item along with a uniqueidentifier that can be used to match any other body model to theirs. Abuyer 1301 looking for clothing provides their unique body identifierand the matching component 1304 compares the 3D body shapes andancillary data (including optional ratings of clothing fit) retrievedfrom a database 1302 to determine the match score 1305. Given aplurality of other matches from other fit models 1307 a display andranking software component 1308 sorts the items for sale based on thematch score 1305 (how similar their body is to the seller's). Thismethod for sizing clothing applies to any retail application where a fitmodel for each clothing size is scanned and the associated bodyidentifier is used to determine whether a new individual will fit thatsize. A score of the quality of fit (based on the body match score) canbe presented or a threshold on the match score can be used to identifyone (or a small number of) size(s) (i.e. fit models) that will fit theuser's body. This method is analogous to having a friend or personalshopper who is the buyer's size and shape and who tries on clothing forthem to see if it fits before recommending it.

Matching and Sizing Using a Community of Fit Models

More generally, there may be a large database of people who have triedon the same (or similar) garment and each of them can be viewed as a fitmodel; every person in the database can be a fit model for any productassociated with them. The match distance (Section 9) between bodiesincorporates shape and other attributes. Attributes can include one ormore ratings of the product (for fit, style, value, etc.). The totalmatch score can then include a term for the fit rating indicatingwhether the garment fits the fit model. Alternatively, the match can beperformed on body shape and an aggregate fit rating for the matchedbodies computed (Section 10d). If the matched bodies have associatedreviews for the product stored in the database, these reviews may beoptionally displayed to the user such that they are optionally ranked bymatch score.

In an alternative embodiment, the match similarity is computed onlybased on product information (brand, style, size) using the ancillary orproduct distance function (Section 9). A user selects a particulargarment and a list of matches (IDs) is generated from the database whereeach ID corresponds to a person who has purchased and/or rated theproduct. The body shapes of the matching IDs are compared to the user'sbody shape by computing the body shape match score. An aggregate of allthese scores is computed; for example by computing the mean score. Thisscore is presented to the user (e.g. on a 100-point scale) to indicatehow well the garment may fit them.

Automatically Obtaining Fit for Clothing Presented on a Web Page

A method is described for automatically determining the fit of a garmentpresented on a retail website. This method uses the techniques above formatching a user's body to a database of other bodies that have tried onsimilar garments. These methods are augmented with a means fordetermining relevant clothing brand, style and size information from awebsite. Referring to FIG. 14, the user's web browser 1401 is augmentedto run software implementing the size determining process. This softwaremay be installed on the user's computer and activated by a buttoninstalled, for example in the browser toolbar. When activated, theproduct determining process 1403 extracts the URL of the web page andthe HTML source of the page. It parses these to extract the brand andidentifying product codes; note that product ID codes are oftenexplicitly part of the URL making their extraction straightforward. Adatabase of known product codes 1404 for different brands may be used tointerpret the HTML and URL data.

When the user clicks a button to obtain their size for a given garment,the size determining process 1405 obtains their unique body identifier.The unique identifier for the user's body model may be stored on theircomputer hard disk or memory, for example, in the form of a “cookie”1402. Alternatively, if no cookie is present, the user is asked toprovide authenticating information such as a username and password. Onceidentified, the body shape of the user is known.

The size determining process 1405 searches a database 1406 for peoplewith similar bodies who have purchased or rated the clothing item asdetermined by the product determining process 1403. The match score(Section 9) is computed and the N best matches are identified. Thenumber of matches can vary but the default setting in one embodiment is10. Ratings and comments stored with the N matches may be displayed.Alternatively the size preferences of these N bodies may be combined(Section 10d) to recommend a particular size for the determined product.

Optionally, this size can be inserted automatically into a web formusing a size entry process. The size entry process determines the sizefields in the HTML source and sets the appropriate values based on thedetermined size.

Custom Clothing

Measurements extracted from the body (Section 10) can be used as inputto standard pattern generation software for custom clothing or toon-line forms for ordering custom (or semi-custom) clothing.

Shape-Aware Advertising

A shape-sensitive advertising component uses the body model inconjunction with on-line (or cell phone) web browsing and shopping.Based on a person's body shape, advertising (e.g. banner ads in a webbrowser) may vary. The system uses body shape matching (Section 9) (orextracted properties such as measurements (Section 10)) to associateparticular advertisements with particular body shapes.

For example, advertisers can select a range of body shapes that fittheir product demographics (e.g. heavy men or short women). Thebody-shape matching component matches advertiser specifications withbody shapes and presents shape-targeted advertisements (e.g. for weightloss or plus-sized clothing). For example, an advertiser may specify agender, height and weight range, a bust size, etc. Advertisers may alsospecify body shapes based on example 3D body models selected from anelectronic presentation of different body shapes or by providing a fitmodel scan. These exemplar bodies are then used to produce a match score(Section 9) that determines how similar a user is to the exemplarspecification.

Referring to FIG. 15, body shape information about a user may be storedon the user's computer; for example in the form of a “cookie” 1502. Whenbrowsing a website depicted at 1501, this cookie provides a uniqueidentifier to an ad manager software component 1503. The ad managersoftware component 1503 retrieves information about the body from a bodymodel database 1504 using the unique identifier. The ad manager softwarecomponent can keep the identity of the user private and communicategeneral information about their body shape to a shape-sensitive adexchange software component 1505. This information may include bodyshape coefficients, the ID of a similar exemplar body, measurements suchas height or weight, demographic information such as age and gender, andshape category information such as athletic or heavy build. It should beunderstood that standard ad targeting information can also be suppliedsuch as IP address, geographic location and historical click/purchaseinformation.

The shape-sensitive ad exchange component 1505 matches the shapeinformation about a user to a database of advertiser requests 1506. Ifthere are multiple matching advertisements, one or more of the matchingadvertisements is selected for display. The mechanism for selection canbe randomized or can take into account how much an advertiser is willingto pay. The rate for each advertisement may vary depending on theoverall quality of the match score (i.e. how close the user'smeasurements are to the target shape specified by the advertiser). Astandard bartering or auction mechanism may be used for advertisers tocompete for presentation to matched users.

Statistics of purchases and advertising-related click histories forpeople of particular body shapes are collected and stored in a database1504. Matches to the body shapes of other shoppers or website users canalso be used to target advertising based on the purchases of otherpeople of similar shape. This is achieved by finding similar body shapesusing the body shape matching component and accessing the storedshopping and clicking statistics for people of similar shape. If aperson of a particular shape has clicked on an advertisement, anadvertiser may pay more for presentation to a similarly shaped person.Any website can be enabled with this shape-sensitive advertising featureusing cookies. Users can disable this feature by changing their browserpreferences. This shape feature can be combined with other commonlyacquired information about shopping and clicking behavior used for thepresentation of personalized or targeted advertising.

Virtual Try On

The estimated body shape model can also be used to try on virtualclothing. There are several computer graphics methods, includingcommercial products, for simulating clothing draped on 3D bodies andthese are not discussed here. The body model can be saved in any one ofthe common graphics model formats and imported into a standard clothingsimulation software system.

An alternative embodiment for virtual clothing try-on uses thebody-shape matching component (Sections 9 and 10d) to match a user'sbody shape to body shapes stored in a database. Virtual try on isenabled by collecting a database of models of different shapes and sizeswearing a plurality of clothing items. When the user wants to see howthey will look in a particular clothing item, the database of storedmodels is searched for the closest matching body shape for which animage (or graphic representation) of the model in that item exists. Thisimage is then displayed to the user. In this way, each person visiting aretail clothing website may see the same merchandise but on differentmodels (models that look most like them). This provides the equivalentof a personalized clothing catalog for the person's shape. This is aform of “example-based virtual clothing”. Rather than rendering clothingusing graphics, many images of models are stored and recalled as needed.The key concept is that this recall is based on similarity of bodyshape.

Other Applications

There many applications for body shape extraction from images. Severalare described below.Forensic Analysis. The parametric shape model can be recovered forpeople wearing clothing and used to extract biometric measurements suchas subject height and weight (Section 10). For crime scene videocontaining clothed subjects, this provides important evidence beyondstandard methods. Body shape can also be used for persistentsurveillance. By identifying the shape of people in images, they can betracked over time and when they leave and re-enter the scene, their bodyshape can be used to reestablish tracking and determine identity among agroup of people using the shape distance score.Health care. Certain body shapes are associated with the risk ofcardiovascular disease, metabolic syndrome, diabetes, cancer, etc.Current measurement methods for predicting risk from body shape arelimited (e.g. measurements of waist size). More detailed shapedescriptors (e.g. combinations of measurements) could be used to predictrisk of various diseases. Given a training database of healthmeasurements and fitted shape parameters (or derived measures), themethods in Section 10 are used to learn a mathematical model predictingthe health measurements from the shape measurements. The simplestembodiment uses linear regression as described in Section 10 though morecomplex non-linear (or multi-linear) models may be used. Non-parametricmatching may also be used (Section 10d).

Also automatic tracking of the elderly and the ill in naturalenvironments is widely recognized to be valuable. No current methodsprovide detailed 3D body pose and shape measurements for clothed people.Unlike a laboratory or clinical setting, in-home tracking involves thecomputation of body pose of people in clothing. Multiple calibratedcameras in a home (or other residential setting) provide image features(e.g. foreground silhouettes) for fitting the shape model using theclothing-robust method. A stereo map of the home environment can bebuilt from the multiple cameras and used to predict regions of the worldin which the body is occluded (e.g. by furniture). The activity of theperson can be assessed by the amount of motion over time. For example,the range of motion of each joint throughout the day can be computed.Tremor (e.g. in people with Parkinson's disease) can be assessed overtime by an analysis of the high frequency motion of the person. Changesin posture or weight can be detected by comparing body model parametersestimated over long time spans.

SECTION 13. REFERENCES

The following references, including the disclosures thereof, areincorporated herein by reference in their entirely.

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The functions described herein may be embodied as computer implementedinventions in which software stored in a memory is executed by aprocessor to implement the respective functions. Furthermore, thefunctions described herein may be implemented by one or more processorsexecuting one or more software programs out of a memory, via a digitalsignal processor or a combination of both a processor and a digitalsignal processor. Additionally, it should be recognized that selectedfunctions may be performed by the processor while other selected formsare executed via a digital signal processor. Additionally, one or moreselected functions described herein may alternatively be embodied inhardware components or embedded in firmware.

It will be appreciated by those of ordinary skill in the art thatmodifications to and variations of the above described system and methodmay be made without departing from the inventive concepts disclosedherein. Accordingly, the invention should not be viewed as limitedexcept by the scope and spirit of the appended claims.

1. A computer implemented method of estimating a shape of a body of anindividual, comprising the steps of: obtaining input data including datarepresenting said body in a plurality of poses; and fitting a parametricbody model of said body to the data representation of said bodycontained in the input data in said plurality of poses to generatemultiple sets of pose parameters and at least one set of shapeparameters, said at least one set of shape parameters being consistentwith said plurality of poses.
 2. The method of claim 1 wherein thefitting of said parametric body model to the data representation of saidbody includes optimizing an objective function defined at least in partby said multiple sets of pose parameters and said at least one set ofshape parameters.
 3. The method of claim 1 wherein said individual hasone or more of an associated gender and an associated ethnicity, andwherein the fitting of said parametric body model to the datarepresentation of said body includes optimizing an objective functiondefined at least in part by said multiple sets of pose parameters, saidat least one set of shape parameters, and at least one specifiedparameter corresponding to one or more of the gender and the ethnicityof said individual.
 4. The method of claim 1 wherein the obtaining ofsaid input data includes obtaining said input data from one or moreinput devices selected from the group consisting of a camera, a rangesensor, and an infrared sensor.
 5. The method of claim 1 wherein theobtaining of said input data includes obtaining data representing atleast a partially clothed body of an individual in a plurality of poses.6. The method of claim 5 wherein the fitting of said parametric bodymodel includes fitting a parametric body model of said at least apartially clothed body to the data representation of said at least apartially clothed body to generate parameters indicative of anestimation of a naked body shape of said at least a partially clothedbody.
 7. The method of claim 6 wherein the fitting of said parametricbody model of said at least a partially clothed body utilizes anobjective function that permits the estimated naked body shape to besubstantially within the data representation of the clothed portion ofthe body.
 8. The method of claim 1 wherein said parametric body model isa statistical parametric body model.
 9. A computer implemented method ofestimating a shape of a body of an individual, comprising the steps of:obtaining input data including data representing a body of an individualin at least one pose, said body being at least partially clothed;detecting, using the data representation of said body, at least aclothed portion of the data representation of said body, the clothedportion having an associated looseness characteristic; and obtaining anestimation of body shape under at least the clothed portion of said bodyby optimizing an objective function based at least in part on thelooseness characteristic.
 10. The method of claim 9 wherein theoptimizing of said objective function includes optimizing said objectivefunction based at least in part on at least one set of pose parametersand a set of shape parameters, said at least one set of pose parametersand said set of shape parameters at least partially defining aparametric body model of said body.
 11. The method of claim 9 whereinsaid individual has one or more of an associated gender and anassociated ethnicity, and wherein the optimizing of said objectivefunction includes optimizing said objective function based at least inpart on one or more of the gender and the ethnicity of said individual.12. The method of claim 9 wherein the obtaining of said input dataincludes obtaining said input data from one or more input devicesselected from the group consisting of a camera, a range sensor, and aninfrared sensor.
 13. A computer implemented method of estimating a shapeof a body of an individual, comprising the steps of: obtaining one ormore input images from at least one camera, said one or more inputimages containing depictions of said body in at least one pose, said atleast one camera having an associated set of camera calibrationparameters; and obtaining an estimation of the shape of the body of saidindividual by optimizing an objective function based at least in part onthe set of camera calibration parameters.
 14. The method of claim 13further including segmenting each of said one or more input images intoa foreground region and a background region, said foreground regioncontaining the respective depiction of said body in a respective one ofsaid plurality of poses.
 15. The method of claim 14: wherein saidobjective function includes a first objective function corresponding tosaid foreground region of the respective input images, and a secondobjective function corresponding to said background region of therespective input images; and wherein the optimizing of said objectivefunction includes optimizing a sum of said first objective function andsaid second objective function.
 16. The method of claim 15 wherein theoptimizing of said objective function includes optimizing a weighted sumof said first objective function and said second objective function. 17.The method of claim 15: wherein said background region corresponds to arigid background scene; wherein said method further includes identifyingat least one feature point in the rigid background scene of each of saidone or more input images; wherein said first objective function isdefined at least in part by said multiple sets of pose parameters, saidset of shape parameters, and the set of camera calibration parameters;and wherein said second objective function is defined at least in partby the set of camera calibration parameters and said at least onefeature point in the rigid background scene.
 18. The method of claim 14wherein at least a portion of said background region is moving.
 19. Themethod of claim 15: wherein said objective function includes said firstobjective function, said second objective function, and at least onethird objective function, the third objective function being defined atleast in part by one or more of the set of camera calibrationparameters; and wherein the optimizing of said objective functionincludes optimizing a sum of said first objective function, said secondobjective function, and the third objective function.
 20. The method ofclaim 17: wherein said objective function includes said first objectivefunction, said second objective function, the third objective function,and at least one fourth objective function, the fourth objectivefunction being defined at least in part by an amount of variation in atleast one of the set of camera calibration parameters; and wherein theoptimizing of said objective function includes optimizing a sum of saidfirst objective function, said second objective function, the thirdobjective function, and the fourth objective function.
 21. The method ofclaim 18 wherein the optimizing of said objective function includesoptimizing a weighted sum of said first objective function, said secondobjective function, the third objective function, and the fourthobjective function.
 22. The method of claim 17: wherein said objectivefunction includes said first objective function, said second objectivefunction, the third objective function, the fourth objective function,and at least one fifth objective function, the fifth objective functionbeing defined at least in part by an amount of variation in at least oneof said plurality of poses; and wherein the optimizing of said objectivefunction includes optimizing a sum of said first objective function,said second objective function, the third objective function, the fourthobjective function, and the fifth objective function.
 23. The method ofclaim 22 wherein the optimizing of said objective function includesoptimizing a weighted sum of said first objective function, said secondobjective function, the third objective function, the fourth objectivefunction, and the fifth objective function.
 24. The method of claim 13:wherein said objective function includes said first objective function,and at least one second objective function, said at least one secondobjective function being defined at least in part by an amount ofvariation in at least one of said plurality of poses; and wherein theoptimizing of said objective function includes optimizing a sum of saidfirst objective function and said at least one second objectivefunction.
 25. The method of claim 14: wherein each of said one or moreinput images depicts said body disposed in front of a first surfacewithin said background region, said first surface having a predeterminedmulti-color pattern disposed thereon; and wherein said method furtherincludes calculating at least one of the set of camera calibrationparameters using said first surface.
 26. The method of claim 14: whereineach of said one or more input images depicts said body disposed infront of a first surface and a second surface, each of the first andsecond surfaces being within said background region, each of the firstand second surfaces having a predetermined multi-color pattern disposedthereon; and wherein said method further includes calculating at leastone of the set of camera calibration parameters based on at least onehomography between the camera and at least one of the first and secondsurfaces.
 27. The method of claim 26: wherein each of the first andsecond surfaces having said predetermined multi-color pattern disposedthereon has an associated color distribution; and wherein the segmentingof each of said one or more input images into said foreground region andsaid background region includes segmenting each of said one or moreinput images based at least in part on the color distribution associatedwith at least one of the first and second surfaces.
 28. The method ofclaim 13 wherein said at least one camera is moving and said body isstill.
 29. The method of claim 13 wherein said at least one camera isstill and said body is moving.
 30. The method of claim 13 wherein bothof said at least one camera and said body are moving.
 31. A computerimplemented method of estimating a shape of a body of an individual,comprising the steps of: obtaining input data including datarepresenting said body in at least one pose, said body having at leastone associated attribute, the at least one attribute of said body beingsubject to at least one constraint; fitting a parametric body model ofsaid body to the data representation of said body while substantiallysatisfying said at least one constraint on the at least one attribute ofsaid body, said parametric body model being defined by a plurality ofparameters including at least one set of pose parameters and a set ofshape parameters, whereby said parametric body model has an associatedshape that is representative of the shape of the body of saidindividual.
 32. The method of claim 31 wherein said at least oneconstraint is operative to constrain the at least one attribute of saidbody to at least one fixed value.
 33. The method of claim 32: whereinthere is a predetermined linear relationship between the at least oneattribute of said body and said set of shape parameters; and whereinsaid method further includes calculating the at least one attribute ofsaid body from said set of shape parameters based on said predeterminedlinear relationship.
 34. The method of claim 31 wherein the fitting ofsaid parametric body model to the data representation of said bodyincludes optimizing a first objective function defined at least in partby said at least one set of pose parameters and said set of shapeparameters.
 35. The method of claim 34 wherein the fitting of saidparametric body model to the data representation of said body includesoptimizing a sum of said first objective function and at least onesecond objective function, the second objective function being definedat least in part by the at least one attribute of said body.
 36. Themethod of claim 34 wherein the fitting of said parametric body model tothe data representation of said body includes optimizing a sum of saidfirst objective function and at least one second objective function, thesecond objective function being defined at least in part by the at leastone attribute of said body and a third function, said third functionbeing defined by said set of shape parameters.
 37. The method of claim34 wherein the fitting of said parametric body model to the datarepresentation of said body includes optimizing a sum of said firstobjective function and at least one second objective function, thesecond objective function being defined at least in part by the at leastone attribute of said body and a third function, said third functionbeing defined by said set of shape parameters, said third function beingoperative to predict at least one of the at least one attribute of saidbody based on said set of shape parameters.
 38. A computer implementedmethod of obtaining camera calibration and image segmentation,comprising the steps of: obtaining, from at least one camera, image dataassociated with at least one image of an object in front of at least onesurface, said at least one surface having a predetermined multi-chromapattern with predetermined pattern dimensions; in a first processingstep, processing the image data from the at least one image of saidobject to obtain one or more intrinsic or extrinsic parametersassociated with the camera; and in a second processing step, utilizingthe same image data associated with the at least one image of saidobject, performing segmentation to segment a foreground image of theobject from said at least one surface.
 39. The method of claim 38further including generating an estimation of one or more of objectshape and pose utilizing the intrinsic or extrinsic parameters and thesegmented foreground image obtained in the first and second processingsteps, respectively.
 40. The method of claim 38 wherein the image has anassociated foreground region and an associated background region,wherein the image includes a plurality of pixels, and wherein saidmethod further includes: calculating, using said predeterminedmulti-chroma pattern disposed on said at least one surface, a colordistribution for said at least one surface; determining, based on therespective color distribution for said at least one surface, alikelihood that each of said plurality of pixels in the image depicts aportion of said at least one surface; for each pixel having a lowlikelihood of depicting a portion of said at least one surface,segmenting the respective pixel to said foreground region of the image;and otherwise, segmenting the respective pixel to said background regionof the image.
 41. The method of claim 40 further including calculating,from the color distribution for said at least one surface, a probabilityimage for said at least one surface, wherein each probability image isoperative to provide an indication of a probability of one of saidplurality of pixels being generated from the color distribution of saidat least one surface.
 42. The method of claim 41 further includingcalculating a per-pixel maximum of the probability images.
 43. Themethod of claim 42 wherein the segmenting of the respective pixelsincludes thresholding said per-pixel maximum of the probability images.44. The method of claim 42 wherein said predetermined multi-chromapattern is a checkerboard pattern.
 45. The method of claim 44 whereinsaid checkerboard pattern is blue and green.
 46. The method of claim 38wherein said object at least partially occludes said at least onesurface.
 47. The method of claim 46 wherein said object is selected fromthe group consisting of an inanimate object, a person, and an animal.48. A computer implemented method of estimating a measurement associatedwith a body of an individual, said body having an associated shape andat least one associated attribute, comprising the steps of: obtaining amapping of a representation of the shape of the body of said individualto the at least one attribute of said body; obtaining body shapeinformation pertaining to the shape of the body of said individual; andestimating at least one characteristic associated with the body of saidindividual using the body shape information for said individual and themapping of said representation of the shape of the body of saidindividual to the at least one attribute of said body.
 49. The method ofclaim 48: wherein the body shape information for said individualincludes a set of shape parameters defining, at least in part, aparametric body model for the body of said individual; and wherein theestimating of said at least one characteristic includes estimating saidat least one characteristic using said set of shape parameters for saidparametric body model.
 50. The method of claim 49 wherein saidparametric body model has a plurality of vertex coordinates associatedtherewith, and wherein the obtaining of the mapping of therepresentation of the shape of said body to the at least one attributeof said body includes identifying at least a portion of said pluralityof vertex coordinates for said parametric body model, and learning afunction for performing a parametric or non-parametric mapping of thevertex coordinates to the at least one attribute of said body.
 51. Themethod of claim 50 wherein the learning of said function for mapping thevertex coordinates to the at least one attribute includes learning saidfunction using a linear regression technique.
 52. The method of claim 49wherein said parametric body model has a plurality of measurementsassociated therewith, and wherein the obtaining of the mapping of therepresentation of the shape of said body to the at least one attributeof said body includes identifying at least a portion of said pluralityof measurements for said parametric body model, and learning a functionfor performing a parametric or non-parametric mapping of themeasurements to point locations on said parametric body model.
 53. Themethod of claim 52 wherein the learning of said function for mapping themeasurements to the point locations includes learning said functionusing a linear regression technique.
 54. The method of claim 48 whereinthe obtaining of the mapping of the representation of the shape of thebody of said individual to the at least one attribute of said bodyincludes a set of shape parameters
 55. The method of claim 48 whereinthe estimating of said at least one characteristic is performed inassociation with one or more of a virtual try-on of clothing by saidindividual, a purchase of clothing for said individual, and an animationof a representation of said individual.
 56. A method of matchingattributes associated with bodies of a plurality of individuals,comprising the steps of: obtaining input data representing a body of afirst individual; generating, using said input data, informationdefining a parametric body model of said first individual, theparametric body model of said first individual having at least oneassociated attribute; accessing, from a database, information definingat least one parametric body model of at least one second individual,the parametric body model of the second individual having at least oneassociated attribute; computing a measure of similarity between the atleast one attribute of the parametric body model of said firstindividual and the at least one attribute of said at least oneparametric body model of said at least one second individual; andgenerating a value indicative of the similarly between the attributes ofthe parametric body models of the first and second individuals based atleast in part on the computed measure of similarity.
 57. The method ofclaim 56 wherein the at least one attribute corresponds to at least oneshape coefficient.
 58. The method of claim 56: wherein each of theparametric body model of said first individual and the at least oneparametric body model of said at least one second individual has aplurality of associated vertex locations; wherein each of the parametricbody model of said first individual and the at least one parametric bodymodel of said at least one second individual defines a mesh; whereineach of the at least one parametric body model of said at least onesecond individual is in alignment with the mesh of the parametric bodymodel of said first individual; and wherein the computing of saidmeasure of similarity includes computing distances between selected onesof the vertex locations of the parametric body model of said firstindividual and corresponding ones of the vertex locations of the atleast one parametric body model of said at least one second individual.59. The method of claim 56: wherein the accessing of said informationincludes accessing information defining a plurality of parametric bodymodels of a plurality of second individuals, respectively; wherein thecomputing of said measure of similarity includes computing multiplemeasures of similarity between the at least one attribute of theparametric body model of said first individual and the attributes of therespective parametric body models of the plurality of secondindividuals; and wherein said method further includes generating, usingsaid multiple measures of similarity, a ranking of the similaritybetween the at least one attribute of the parametric body model of saidfirst individual and the attributes of the respective parametric bodymodels of the plurality of second individuals.
 60. The method of claim56 further including estimating at least one measurement associated withthe body of said first individual based at least in part on the computedmeasure of similarity between the at least one attribute of theparametric body model of said first individual and the at least oneattribute of the parametric body model of the second individual.
 61. Themethod of claim 60 wherein the estimating of said at least onemeasurement associated with the body of said first individual isperformed in association with a purchase of clothing for said firstindividual.
 62. The method of claim 56 further including generating arecommendation pertaining to one or more of a clothing attribute, a bodymeasurement attribute, and a body shape attribute based on said valueindicative of the similarly between the respective attributes.
 63. Themethod of claim 56 further including executing at least one applicationthat uses said value in a decisional process.
 64. A computer implementedmethod of estimating a shape of a body of an individual, comprising thesteps of: obtaining a database containing body shape information, bodypose information, and feature information, said body shape informationpertaining to shapes of a plurality of bodies of individuals, said bodypose information pertaining to poses associated with said plurality ofbodies, said feature information comprising at least one transformationof real or simulated sensor data for each of said plurality of bodies;generating, using said body shape information, said body poseinformation, and said feature information contained in said database, amapping of feature information to body shape and pose information;obtaining input sensor data representing the body of said individual;obtaining feature information for said individual from said input sensordata, said feature information for said individual comprising at leastone transformation of said input sensor data for the body of saidindividual; and estimating, using the feature information for saidindividual and said mapping of feature information to body shape andpose information, the shape of the body of said individual.
 65. Themethod of claim 64 further including: generating information defining a3-dimensional parametric body model having an associated shapecorresponding to the shape of the body of said individual; producing a2-dimensional silhouette of said parametric body model of the body ofsaid individual, said silhouette having an associated contour; andwherein the obtaining of the feature information for said individualincludes obtaining the feature information for said individual from thecontour of the 2-dimensional silhouette.
 66. The method of claim 64further including: obtaining input data representing the body of saidindividual in 3-dimensions; and wherein the obtaining of the featureinformation for said individual includes obtaining the featureinformation for said individual from said data representing the body ofsaid individual in 3-dimensions.
 67. The method of claim 66 furtherincluding generating, using said input data, information defining a3-dimensional parametric body model having an associated shapecorresponding to the shape of the body of said individual.
 68. Acomputer implemented method of determining an indication of a productassociated with a human body, comprising the steps of: obtaining arepresentation of at least one aspect of a body of an individual;comparing the representation of the at least one aspect of the body ofsaid individual to at least one representation of at least one aspect ofeach of a plurality of bodies of different individuals contained in adatabase, wherein each representation associated with each of thedifferent individuals has a product associated therewith; and obtaininga ranking of similarity of the representation of the at least one aspectof the body of said individual to the representation of the at least oneaspect of the bodies of said plurality of different individuals.
 69. Themethod of claim 68 further including selecting, based upon the rankingof similarity, at least one advertisement for at least one product. 70.The method of claim 68 further including displaying, based upon theranking of similarity, a graphical image of at least one productassociated with one of the different individuals.
 71. The method ofclaim 68: wherein each of the body of said individual and the bodies ofthe different individuals is represented by a parametric body model;wherein the comparing of said representation of the at least one aspectof the body of said individual to said at least one representation of atleast one aspect of each of said plurality of bodies of differentindividuals includes computing multiple measures of similarity betweenthe shape of the parametric body model of said individual and the shapesof the parametric body models of the respective different individuals;and wherein said method further includes generating, using said multiplemeasures of similarity, a ranking of the similarity between the shape ofthe parametric body model of said individual and the shapes of theparametric body models of the respective different individuals.
 72. Themethod of claim 71 further including outputting an indication of saidranking on a display.
 73. The method of claim 71 further includingestimating at least one measurement associated with the body of saidindividual based at least in part on the computed measures of similaritybetween the shape of the parametric body model of said individual andthe shapes of the parametric body models of the respective differentindividuals.
 74. The method of claim 73 further including outputting anindication of said at least one measurement on a display or using saidat least one measurement as an input to at least one application.
 75. Asystem for estimating a shape of a body of an individual, comprising: aninput device operative to obtain input data including data representingsaid body in a plurality of poses; and at least one processor operativeto execute at least one program out of at least one memory to fit aparametric body model of said body to the data representation of saidbody contained in the input data in said plurality of poses to generatemultiple sets of pose parameters and at least one set of shapeparameters, said at least one set of shape parameters being consistentwith said plurality of poses.
 76. A system for estimating a shape of abody of an individual, comprising: an input device operative to obtaininput data including data representing a body of an individual in atleast one pose, said body being at least partially clothed; and at leastone processor operative to execute at least one program out of at leastone memory to detect, using the data representation of said body, atleast a clothed portion of the data representation of said body, theclothed portion having an associated looseness characteristic, and togenerate an estimation of body shape under at least the clothed portionof said body by optimizing an objective function based at least in parton the looseness characteristic.
 77. A system for estimating a shape ofa body of an individual, comprising: an input device operative to obtaina plurality of input images from at least one camera, said plurality ofinput images containing depictions of said body in at least one pose,said at least one camera having an associated set of camera calibrationparameters; and at least one processor operative to execute at least oneprogram out of at least one memory to generate an estimation of theshape of the body of said individual by optimizing an objective functionbased at least in part on the set of camera calibration parameters. 78.A system for estimating a shape of a body of an individual, comprising:an input device operative to obtain input data including datarepresenting said body in at least one pose, said body having at leastone associated attribute, the at least one attribute of said body beingsubject to at least one constraint; and at least one processor operativeto execute at least one program out of at least one memory to fit aparametric body model of said body to the data representation of saidbody while substantially satisfying said at least one constraint on theat least one attribute of said body, said parametric body model beingdefined by a plurality of parameters including at least one set of poseparameters and a set of shape parameters, whereby said parametric bodymodel has an associated shape that is representative of the shape of thebody of said individual.
 79. A system for obtaining camera calibrationand image segmentation, comprising: at least one surface having apredetermined multi-chroma pattern with predetermined patterndimensions; an input device operative to obtain, from at least onecamera, image data associated with at least one image of an object infront of said at least one surface; and at least one processor operativeto execute at least one program out of at least one memory: to processthe image data from the at least one image of said object to obtain oneor more intrinsic or extrinsic parameters associated with the camera;and utilizing the same image data associated with the at least one imageof said object, to perform segmentation to segment a foreground image ofthe object from said at least one surface.
 80. The system of claim 79wherein said at least one processor is further operative to execute saidat least one program out of said at least one memory to generate anestimation of object shape utilizing the intrinsic or extrinsicparameters and the segmented foreground image obtained in the first andsecond processing steps, respectively.
 81. A system for estimating ameasurement associated with a body of an individual, said body having anassociated shape and at least one associated attribute, comprising: atleast one processor operative to execute at least one program out of atleast one memory: to receive body shape information pertaining to theshape of the body of said individual; and to estimate at least onecharacteristic associated with the body of said individual using thebody shape information for said individual and a mapping of arepresentation of the shape of the body of said individual to the atleast one attribute of said body.
 82. A system for matching attributesassociated with bodies of a plurality of individuals, comprising: atleast one processor operative to execute at least one program out of atleast one memory: to receive input data representing a body of a firstindividual; to generate, using said input data, information defining aparametric body model of said first individual, the parametric bodymodel of said first individual having at least one associated attribute;to access, from a database, information defining at least one parametricbody model of at least one second individual, the parametric body modelof the second individual having at least one associated attribute; tocompute a measure of similarity between the at least one attribute ofthe parametric body model of said first individual and the at least oneattribute of said at least one parametric body model of said at leastone second individual; and to generate a value indicative of thesimilarly between the attributes of the parametric body models of thefirst and second individuals based at least in part on the computedmeasure of similarity.
 83. A system for estimating a shape of a body ofan individual, comprising: a database containing body shape information,body pose information, and feature information, said body shapeinformation pertaining to shapes of a plurality of bodies ofindividuals, said body pose information pertaining to poses associatedwith said plurality of bodies, said feature information comprising atleast one transformation of sensor data for each of said plurality ofbodies; at least one input device operative to obtain input sensor datarepresenting the body of said individual; and at least one processoroperative to execute at least one program out of at least one memory: togenerate feature information for said individual from said input sensordata, said feature information for said individual comprising at leastone transformation of said input sensor data for the body of saidindividual; to generate, using said body shape information, said bodypose information, and said feature information contained in saiddatabase, a mapping of feature information to body shape and poseinformation; and to estimate, using the feature information for saidindividual and said mapping of feature information to body shape andpose information, the shape of the body of said individual.
 84. A systemfor determining an indication of a product associated with a human body,comprising: at least one processor operative to execute at least oneprogram out of at least one memory: to receive a representation of atleast one aspect of a body of an individual; to compare therepresentation of the at least one aspect of the body of said individualto at least one representation of at least one aspect of each of aplurality of bodies of different individuals contained in a database,wherein each representation associated with each of the differentindividuals has a product associated therewith; and to generate aranking of similarity of the representation of the at least one aspectof the body of said individual to the representation of the at least oneaspect of the bodies of said plurality of different individuals.
 85. Acomputer implemented method of determining attribute similarities,comprising the steps of: receiving input data representing a body of afirst individual; generating, using said input data, informationdefining a parametric body model of said first individual, theparametric body model of said first individual having at least oneassociated attribute; accessing, from a database, informationcorresponding to at least one attribute specification; and in acomputing step, computing a score indicative of a similarity between theat least one attribute associated with the first individual and each ofthe at least one attribute specification.
 86. A system for determiningattribute similarities, comprising: At least one processor operative toexecute at least one program out of at least one memory: to receiveinput data representing a body of a first individual; to generate, usingsaid input data, information defining a parametric body model of saidfirst individual, the parametric body model of said first individualhaving at least one associated attribute; to access, from a database,information corresponding to at least one attribute specification; andto compute a score indicative of a similarity between the at least oneattribute associated with the first individual and each of the at leastone attribute specification.